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commensurable(1)
content(3)
crystals(3)
curve(18)
doc(23)
dq(33)
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field(1)
g2c(57)
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group(177)
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Recently modified knowls
A
mf.gl2.history
A brief history of $\textrm{GL}(2)$ modular forms
curve.highergenus.aut.group_action
A group acting on a compact Riemann Surface
lfunction.history
A history of L-functions
doc.secret
A list of not so secret urls that aren't advertized
intro.tutorial
A tour of the Riemann zeta function
ring.a-field
$A$-field
group.a_group
A-group
ec.q.abc_quality
$abc$ quality
belyi.abc
abc triple for Belyi maps
group.abelian
Abelian group
nf.abelian
Abelian number field
ag.abelian_surface
Abelian surface
av.fq.one_rational_point
Abelian varieties with one rational point
ag.abelian_variety
Abelian variety
group.abelianization
Abelianization
group.abelianization_isolabel
Abelianization label
varieties.about
About varieties
g2c.abs_discriminant
Absolute discriminant
nf.abs_discriminant
Absolute discriminant of a number field
modlgal.absolute_frobenius
Absolute Frobenius
group.galois.absolute
Absolute Galois group
nf.absolute_value
Absolute value of a field
modlgal.absolutely_irreducible
Absolutely irreducible
group.name
Abstract group name
rcs.ack.groups.abstract
Acknowledgements for abstract groups
rcs.ack.modcurve
Acknowledgements for modular curve data
rcs.ack.maass_rigor
Acknowledgements for rigorous Maass forms
rcs.ack.mf.siegel
Acknowledgements for Siegel modular forms
rcs.ack.lfunction.curve
Acknowledgments for (non-elliptic) curve L-functions
rcs.ack.av.fq
Acknowledgments for abelian varieties over finite fields
rcs.ack.artin
Acknowledgments for Artin representations
rcs.ack.belyi
Acknowledgments for Belyi maps
rcs.ack.mf.bianchi
Acknowledgments for Bianchi modular forms
rcs.ack.cmf
Acknowledgments for classical modular forms
rcs.ack.curve.highergenus.aut
Acknowledgments for curves of higher genus with automorphism group data
rcs.ack.character.dirichlet
Acknowledgments for Dirichlet characters
rcs.ack.lfunction.ec
Acknowledgments for elliptic curve L-functions
rcs.ack.ec
Acknowledgments for elliptic curves over number fields
rcs.ack.ec.q
Acknowledgments for elliptic curves over $\Q$
rcs.ack.gg
Acknowledgments for Galois groups
rcs.ack.g2c
Acknowledgments for genus 2 curves
rcs.ack.mf.hilbert
Acknowledgments for Hilbert modular forms
rcs.ack.hosting
Acknowledgments for hosting
rcs.ack.hgm
Acknowledgments for hypergeometric motive data
rcs.ack.lfunction
Acknowledgments for L-functions
rcs.ack.lfunction.maass
Acknowledgments for Maass form L-functions
rcs.ack.maass
Acknowledgments for Maass forms
rcs.ack.meetings
Acknowledgments for meetings
rcs.ack.lfunction.modular
Acknowledgments for modular form L-functions
rcs.ack.nf
Acknowledgments for number fields
rcs.ack.lf
Acknowledgments for p-adic fields
rcs.ack.st_group
Acknowledgments for Sato-Tate groups
rcs.ack.software
Acknowledgments for software
rcs.ack.sponsors
Acknowledgments for sponsors
group.fuchsian.action
Action of $\SL(2,\R)$ in the upper half-plane
rcs.ack.general
Additional acknowledgments
ec.additive_reduction
Additive reduction
ag.affine_space
Affine space
nf.algebraic_closure
Algebraic closure of a field
ag.curve
Algebraic curve
mf.gl2.history.varieties
Algebraic varieties
ag.variety
Algebraic variety
group.almost_simple
Almost simple group
group.alternating
Alternating group
group.ambient
Ambient group
group.ambient_isolabel
Ambient group label
st_group.ambient
Ambient group of a Sato-Tate group
nf.class_number_formula
Analytic class number formula
lfunction.analytic_conductor
Analytic conductor
cmf.analytic_conductor
Analytic conductor of a classical newform
ec.analytic_sha_order
Analytic order of Ш
ec.q.analytic_sha_order
Analytic order of Ш
g2c.analytic_sha
Analytic order of Sha
ec.q.analytic_sha_value
Analytic order of Sha (numerical value)
cmf.analytic_rank
Analytic rank
lfunction.analytic_rank
Analytic rank
modcurve.rank
Analytic rank
mf.bianchi.anr
Analytic rank of a Bianchi newform
g2c.analytic_rank
Analytic rank of a curve
ec.q.analytic_rank
Analytic rank of an elliptic curve over $\Q$
av.fq.angle_rank
Angle rank of a set
af
Arithmetic function
ag.arithmetic_genus
Arithmetic genus
hmsurface.arithmetic_genus
Arithmetic genus
lfunction.arithmetic
Arithmetic L-function
nf.arithmetically_equivalent
Arithmetically equivalent fields
gg.arithmetically_equivalent
Arithmetically equivalent siblings
cmf.artin_field
Artin field
cmf.artin_image
Artin image
artin.lfunction
Artin L-function
lfunction.history.artin
Artin L-functions
artin
Artin representation (definition)
artin.stem_field
Artin stem field
ring.associate
Associate of an element
lf.associated_inertia
Associated inertia
alg.binary_operation.associative
Associative binary operation
nf.assuming_grh
Assuming GRH
cmf.atkin-lehner
Atkin-Lehner involution $w_Q$
group.autjugacy_class
Autjugacy class
group.autjugate_subgroup
Autjugate subgroups
mf.siegel.automorphic_type
Automorphic type
ag.aut_group
Automorphism group
av.aut_group
Automorphism group
curve.highergenus.aut.characters
Automorphism group characters
lf.automorphism_group
Automorphism group of a field extension
g2c.aut_grp
Automorphism group of an algebraic curve
lattice.automorphism_group
Automorphism group of an integral lattice
group.automorphism
Automorphisms of a group
mf.siegel.extent.kp
Available samples for $M_2(K(p))$
mf.siegel.extent.sp4z
Available samples for $M_k(\mathrm{Sp}(4,\mathbb{Z}))$
mf.siegel.extent.sp6z
Available samples for $M_k(\mathrm{Sp}(6,\mathbb{Z}))$
mf.siegel.extent.sp8z
Available samples for $M_k(\mathrm{Sp}(8,\mathbb{Z}))$
mf.siegel.extent.sp4z_2
Available samples for $M_{k,2}(\mathrm{Sp}(4,\mathbb{Z}))$
B
cmf.bad_prime
Bad prime
lfunction.bad_prime
Bad prime
ec.bad_reduction
Bad reduction of an elliptic curve at a prime
ag.base_change
Base change
ec.base_change
Base change
mf.base_change
Base change of a GL(2) modular form
ag.base_field
Base field
belyi.base_field
Base field of a Belyi map
modlgal.base_ring_characteristic
Base ring characteristic
mf.bianchi.base_change
Base-change Bianchi modular forms
character.dirichlet.basic_properties
Basic properties of Dirichlet characters
av.fq.bass_zfv
Bass Frobenius order
belyi.galmap
Belyi map
belyi.label
Belyi map label
belyi.orders
Belyi permutation triple orders
af.bernoulli_numbers
Bernoulli numbers
mf.bianchi.bianchigroup
Bianchi Groups
mf.bianchi
Bianchi modular form
mf.bianchi.bianchimodularforms
Bianchi modular forms
mf.bianchi.newform
Bianchi newform
alg.binary_operation
Binary operation
ec.q.bsdconjecture
Birch and Swinnerton-Dyer conjecture
ec.q.bsd_invariants
Birch and Swinnerton-Dyer invariants of an elliptic curve/$\mathbb{Q}$
ec.bsdconjecture
Birch Swinnerton-Dyer conjecture
shimcurve.b
$B\langle i,j\rangle$
gl2.borel
Borel subgroup
curve.highergenus.aut.braid_equivalence
Braid Equivalence
curve.highergenus.aut.branchpoints
Branch Points
g2c.bsd_invariants
BSD invariants
stats.buckets
Buckets for statistics
hgm.bezout_determinant
Bézout determinant
alg.bezout_matrix
Bézout matrix
hgm.bezout_matrix
Bézout matrix of a hypergeometric motive
hgm.bezout_module
Bézout module of a hypergeometric motive
C
nf.polredabs
Canonical defining polynomial for number fields
modcurve.canonical_field
Canonical field of definition of a modular curve
ec.q.canonical_height
Canonical height
ag.canonical_height
Canonical height of an abelian variety
ec.canonical_height
Canonical height on an elliptic curve
ag.canonical_model
Canonical model
gl2.cartan
Cartan subgroup
lattice.catalogue_of_lattices
Catalogue of Lattices
group.center_isolabel
Center label
group.representation.center
Center of a character
group.center
Center of a group
lfunction.central_character
Central character of an L-function
lfunction.central_point
Central point of an L-function
group.central_quotient
Central quotient
group.central_quotient_isolabel
Central quotient label
group.central
Central subgroup
lfunction.central_value
Central value of an L-function
group.centralizer
Centralizer of a subgroup
group.subgroup.centralizer
Centralizer of a subgroup
group.representation.character
Character of a group representation
mf.maass.mwf.character
Character of a Maass form
cmf.character
Character of a modular form
gg.character_table.data
Character table data
modlgal.characteristic
Characteristic of a mod-$\ell$ Galois representation
ring.characteristic
Characteristic of a ring
av.fq.weil_polynomial
Characteristic polynomial of an abelian variety over a finite field
modlgal.frobenius_charpoly
Characteristic polynomial of Frobenius
group.characteristic_subgroup
Characteristic subgroup
group.chief_series
Chief series of a group
nf.class_number
Class number of a number field
lattice.class_number
Class number of an integral lattice
cmf
Classical modular form
ag.cluster_picture
Cluster picture
mf.bianchi.cm
CM Bianchi newforms
cmf.cm_form
CM form
nf.cm_field
CM number field
modcurve.cm_discriminants
CM points
cmf.minimal_twist
cmf.minimal_twist
modlgal.codomain
Codomain
modlgalrep.codmain
Codomain
cmf.coefficient_field
Coefficient field for newforms
mf.siegel.coefficient_field
Coefficient field for Siegel newforms
lfunction.coefficient_field
Coefficient field of an L-function
cmf.coefficient_ring
Coefficient ring
mf.siegel.coefficient_ring
Coefficient ring
cmf.hecke_ring_generators
Coefficient ring generator bound
ag.cohen_macaulay_type
Cohen-Macaulay type
mf.gl2.history.combinatorics
Combinatorics and $q$-series
commensurable.group
commensurable group
alg.binary_operation.commutative
Commutative binary operation
group.commutator_isolabel
Commutator label
group.commutator_length
Commutator length
group.commutator_subgroup
Commutator subgroup of a group
group.subgroup.complement
Complement
group.complete
Complete group
lfunction.completed
Completed L-function
rcs.cande.groups.abstract
Completeness and extent of abstract group data
rcs.cande.artin
Completeness and extent of Artin representation data
rcs.cande.gg
Completeness and extent of Galois group data
rcs.cande.nf
Completeness and extent of global number field data
rcs.cande.lf
Completeness and extent of local field data
rcs.cande.maass
Completeness and extent of Maass form data
rcs.cande.maass_rigor
Completeness and extent of rigorous Maass form data
dq.mf.bianchi.extent
Completeness of Bianchi Modular Form data
rcs.cande.mf.bianchi
Completeness of Bianchi modular form data
rcs.cande.cmf
Completeness of Classical Modular Form Data
dq.belyi.extent
Completeness of data for Belyi maps
rcs.cande.belyi
Completeness of data for Belyi maps
rcs.cande.curve.highergenus.aut
Completeness of data for families of higher genus curves with automorphisms
dq.lattice.completeness
Completeness of data for Integral Lattices
rcs.cande.lattice
Completeness of data for Integral Lattices
dq.hgm.extent
Completeness of data on hypergeometric motives
rcs.cande.hgm
Completeness of data on hypergeometric motives
rcs.cande.av.fq
Completeness of data on isogeny classes of abelian varieties over finite fields
rcs.cande.character.dirichlet
Completeness of Dirichlet character data
rcs.cande.ec
Completeness of elliptic curve data
rcs.cande.ec.q
Completeness of elliptic curve data over $\Q$
rcs.cande.g2c
Completeness of genus 2 curve data
dq.mf.hilbert.extent
Completeness of Hilbert modular form data
rcs.cande.mf.hilbert
Completeness of Hilbert modular form data
rcs.cande.hmsurface
Completeness of Hilbert modular surface data
rcs.cande.lfunction
Completeness of L-function Data
rcs.cande.zeros.zeta
Completeness of Riemann Zeta Zeros Data
rcs.cande.st_group
Completeness of Sato-Tate Group Data
st_group.summary
Completeness of Sato-Tate group data
rcs.cande.mf.siegel
Completeness of Siegel modular form data
rcs.cande.modcurve
Completeness of the modular curve database
group.complex_character_table
Complex character table of a finite group
nf.complex_embedding
Complex embedding
cmf.embedding_label
Complex embedding label
group.representation.irrep
Complex irreducible representation
ag.complex_multiplication
Complex multiplication
ec.complex_multiplication
Complex multiplication
mf.cm
Complex multiplication
st_group.component_group
Component group of a Sato-Tate group
hmsurface.component_ideal
Component ideal
st_group.components
Components of a Sato-Tate group
group.division_computing_labels
Computing labels of divisions of a group
g2c.conditional_mw_group
Conditional Mordell-Weil group
av.endomorphism_ring_conductor
Conductor
modlgal.conductor
Conductor
ec.conductor_label
Conductor labels for elliptic curves
character.dirichlet.conductor
Conductor of a Dirichlet character
character.dirichlet.conrey.conductor
Conductor of a Dirichlet character from its Conrey label
g2c.conductor
Conductor of a genus 2 curve
hgm.conductor
Conductor of a hypergeometric motive
nf.conductor
Conductor of an abelian number field
ag.conductor
Conductor of an abelian variety
artin.conductor
Conductor of an Artin representation
ec.conductor
Conductor of an elliptic curve
ec.q.conductor
Conductor of an elliptic curve over $\Q$
lfunction.conductor
Conductor of an L-function
group.representation.cyclotomic_n
Conductor of the field generated by the character values
ec.conductor_valuation
Conductor valuation
cmf.congruence_subgroup
Congruence subgroup
hmsurface.congruence_subgroup
Congruence Subgroup
mf.bianchi.bianchicongruencesubgroup
Congruence subgroup of a Bianchi group
group.sp2gr.subgroup.congn
Congruence subgroup of level $N$ of $\Sp(2g,\Z)$
ec.congruent_number_curve
Congruent number curves
ec.congruent_number_problem
Congruent number problem
ec.congruent_number
Congruent numbers
gg.conjugacy_classes
Conjugacy class
group.conjugacy_class
Conjugacy class
gg.conjugacy_classes.data
Conjugacy class representatives
curve.highergenus.aut.conjugacyclasses
Conjugacy classes
st_group.connected
Connected Sato-Tate group
character.dirichlet.conrey.index
Conrey index of a Dirichlet character
character.dirichlet.conrey
Conrey label of Dirichlet characters
character.dirichlet.conrey.primitive_generator
Conrey primitive generator modulo $p$
artin.permutation_container
Containing permutation representation
modcurve.contains_negative_one
Contains $-I$
group.core
Core of a subgroup
av.fq.frobenius_angles_correctness
Correctness of Frobenius angles
group.coset
Coset of a subgroup
doc.create_knowl
Create a knowl
ec.q.cremona_label
Cremona label
lfunction.critical_line
Critical line of an L-function
lfunction.critical_strip
Critical strip
crystals.crystal
Crystal
hgm.cusp_index
Cusp index
modcurve.cusp_orbits
Cusp orbits
modcurve.cusp_widths
Cusp widths
cmf.cusp_form
Cuspidal modular form
hmsurface.cusps
Cusps
modcurve.cusps
Cusps of a modular curve
group.fuchsian.cusps
Cusps of a subgroup of the modular group
group.cyclic
Cyclic group
ag.cyclic_trigonal
Cyclic trigonal curve
D
clusterpicture.data
Data for a cluster picture
character.dirichlet.data
Data for a dirichlet character
character.dirichlet.orbit_data
Data for a Galois orbit of Dirichlet characters
nf.field.data
Data for a global number field
lf.field.data
Data for a local field
lattice.data
Data for an integral lattice
group.small.data
Data on small group
av.decomposition
Decomposition into isogeny factors
cmf.decomposition.new.gamma0chi
Decomposition into newforms
cmf.dim_decomposition
Decomposition into newforms
cmf.decomposition.new.gamma1
Decomposition into newforms for Gamma1(N)
g2c.decomposition
Decomposition of the Jacobian of a genus 2 curve
ring.dedekind_domain
Dedekind domain
mf.half_integral_weight.dedekind_eta
Dedekind eta function
lfunction.history.dedekind
Dedekind zeta-functions, history
hgm.defining_parameters
Defining parameters of a hypergeometric motive
cmf.defining_polynomial
Defining polynomial
mf.siegel.defining_polynomial
Defining polynomial
lf.defining_polynomial
Defining polynomial of a local field
nf.defining_polynomial
Defining Polynomial of a Number Field
group
Definition of group
lf.qp
Definition of $\Q_p$
ring
Definition of ring
hmsurface.level
Definition of the level
gg.degree
Degree
lfunction.known_degree1
Degree 1 L-functions, all
lfunction.known_degree2
Degree 2 L-functions, examples
lfunction.known_degree3
Degree 3 L-functions, examples
lfunction.known_degree4
Degree 4 L-functions, examples
belyi.degree
Degree of a Belyi map
group.representation.complex_char_deg
Degree of a character
character.dirichlet.degree
Degree of a Dirichlet character
hgm.degree
Degree of a hypergeometric motive
lf.degree
Degree of a local field extension
nf.degree
Degree of a number field
modcurve.point_degree
Degree of a point on a modular curve
st_group.degree
Degree of a Sato-Tate group
mf.siegel.degree
Degree of a Siegel modular form
lfunction.degree
Degree of an L-function
av.deligne_module
Deligne module
lattice.density
Density of an integral lattice
group.derived_series
Derived series of a group
doc.knowl.description
Description field in knowls
cmf.statistics_extent
Description of completeness
artin.determinant
Determinant of an Artin representation
lattice.determinant
Determinant of an integral lattice
doc.development
Developers Guide
group.dicyclic
Dicyclic group
group.dihedral
Dihedral group
cmf.dimension
Dimension
cmf.display_dim
Dimension
mf.siegel.dimension
Dimension
modlgal.dimension
Dimension
modlgalrep.dimension
Dimension
curve.highergenus.aut.dimension
Dimension of a family of curves
cmf.dimension_galois_orbit
Dimension of a Hecke orbit
mf.hilbert.dimension
Dimension of a Hecke orbit
ag.dimension
Dimension of an algebraic variety
artin.dimension
Dimension of an Artin representation
lattice.dimension
Dimension of an integral lattice
cmf.atkin_lehner_dims
Dimensions of Atkin-Lehner subspaces
group.direct_product
Direct product of groups
character.dirichlet
Dirichlet character
artin.dimensionone
Dirichlet character associated with a 1-dimensional Artin representation
dq.character.dirichlet.extent
Dirichlet character data extent
character.dirichlet.group
Dirichlet character group
nf.dirichlet_group
Dirichlet group of an Abelian number field
lfunction.dirichlet
Dirichlet L-function
lfunction.dirichlet_series
Dirichlet series
lfunction.history.dirichlet
Dirichlet's work on L-functions
lf.discriminant_exponent
Discriminant exponent of a local field
g2c.discriminant
Discriminant of a genus 2 curve
nf.discriminant
Discriminant of a number field
shimcurve.discb
Discriminant of a quaternion algebra
shimcurve.disco
Discriminant of a quaternion order
sh.disc
Discriminant of a Shimura curve
ec.discriminant
Discriminant of a Weierstrass equation
ec.q.discriminant
Discriminant of an elliptic curve over $\Q$
nf.poly_discriminant
Discriminant of polynomial
nf.discriminant_root_field
Discriminant root field
lf.discriminant_root_field
Discriminant root field of a local field
ec.discriminant_valuation
Discriminant valuation
cmf.distinguishing_primes
Distinguishing Hecke operators
group.division
Divisions of a group
af.divisor_function
Divisor function
cmf.dualform
Dual cuspform
lattice.dual
Dual lattice
lfunction.dual
Dual of an L-function
modlgal.dual_pair_of_algebras
Dual pair of algebras
mf.siegel.lift.ikeda
Duke-Imamoglu-Ikeda lift
E
lf.eisenstein_polynomial
Eisenstein polynomial
group.elementary
Elementary group
modcurve.elliptic_curve_of_point
Elliptic curve associated to a rational point
ec.invariants
Elliptic curve invariants
ec.q.invariants
Elliptic curve invariants
ec
Elliptic curve over a field
ec.ring
Elliptic curve over a ring
ec.q
Elliptic curve over $\mathbb Q$
mf.gl2.history.elliptic
Elliptic functions
hmsurface.elliptic_point
Elliptic point
modcurve.elliptic_points
Elliptic points
ec.scheme
Elliptic scheme
gg.elusive_group
Elusive group
modcurve.embedded_model
Embedded model
cmf.embedding_format
Embedding Format
cmf.embedding
Embedding of a modular form
nf.embedding
Embedding of a number field
st_group.embedding
Embedding of a Sato-Tate group
ag.endomorphism_algebra
Endomorphism algebra
g2c.end_alg
Endomorphism algebra
av.endomorphism_field
Endomorphism field
g2c.jac_endomorphisms
Endomorphism invariants
g2c.jac_end_lattice
Endomorphism lattice
ec.endomorphism
Endomorphism of an elliptic curve
ag.endomorphism_ring
Endomorphism ring
av.fq.endomorphism_ring_notation
Endomorphism ring notation
ec.endomorphism_ring
Endomorphism ring of an elliptic curve
ec.q.endomorphism_ring
Endomorphism ring of an elliptic curve
shimcurve.enhanced_group
Enhanced group associated to a polarized quaternion order
cmf.eta_quotient
Eta quotient
ring.euclidean_domain
Euclidean domain
g2c.bad_lfactors
Euler factors at bad primes
specialfunction.gamma
Euler gamma function
lfunction.riemann.euler_product
Euler product for the Riemann zeta function
lfunction.euler_product
Euler product of an L-function
lfunction.history.euler
Euler's work on the zeta function
st_group.probabilities
Event probabilities
mf.maass.exceptional_eigenvalue
Exceptional eigenvalues of Maass forms
gl2.exceptional
Exceptional subgroup
doc.view_knowl
Expand a knowl
group.picture_description
Explanation of pictures for abstract groups
portrait.groups.abstract
Explanation of pictures for abstract groups
group.exponent
Exponent of a group
dq.ec.extent
Extent of data for elliptic curves over $\Q$
dq.curve.highergenus.aut.extent
Extent of data for families of higher genus curves with automorphisms
dq.hecke_algebras.extent
Extent of data for Hecke Algebras
dq.lattice.extent
Extent of data for Integral Lattices
dq.rep_galois_modl.extent
Extent of data for mod ℓ Galois representations
dq.modlmf.extent
Extent of data for mod ℓ Modular Forms
dq.charmodl.extent
Extent of data for mod ℓ Characters
dq.ecnf.extent
Extent of elliptic curve data over number fields
gg.extent
Extent of Galois group data
nf.extent
Extent of global number field data
lf.extent
Extent of local number field data
F
group.order_factorization
Factorization of the group order
group.representation.faithful
Faithful representation
ec.q.faltings_height
Faltings height of an elliptic curve
ec.q.faltings_ratio
Faltings ratio
group.families
Families of abstract groups
mf.siegel.family
Family of Siegel groups
modcurve.fiber_product
Fiber product
ring.field
Field
gg.field_automorphisms
Field automorphisms associated with a Galois group
ring.field_of_fractions
Field of fractions of an integral domain
character.dirichlet.value_field
Field of values of a Dirichlet character
field.about
Fields
belyi.search_input
Find a Belyi map
mf.bianchi.search_input
Find a Bianchi modular form
character.dirichlet.search_input
Find a Dirichlet character
curve.highergenus.aut.search_input
Find a family of higher genus curves
gg.search_input
Find a Galois group
g2c.search_input
Find a genus 2 curve
hmsurface.search_input
Find a Hilbert modular surface
hgm.search_input
Find a hypergeometric motive
cmf.search_input
Find a newform or newspace by label
nf.search_input
Find a number field
lf.search_input
Find a p-adic field
st_group.search_input
Find a Sato-Tate group
group.find_input
Find an abstract group
artin.search_input
Find an Artin representation
ec.q.search_input
Find an elliptic curve
ec.search_input
Find an elliptic curve
lattice.search_input
Find an integral lattice
av.fq.search_input
Find an isogeny class of abelian varieties
lfunction.search_input
Find an L-function by label
mf.hilbert.search_input
Find Hilbert modular form by label
group.lie_type
Finite Lie Group Names
st_group.first_a2_moment
First $a_2$ moment
group.fitting_subgroup
Fitting subgroup of a group
character.dirichlet.field_cut_out
Fixed field of a Dirichlet character
cmf.fouriercoefficients
Fourier coefficients of a modular form
mf.maass.picard.fourierexpansion
Fourier expansion of a Maass form on PSL(2,Z[i])
mf.maass.mwf.fourierexpansion
Fourier expansion of Maass form
mf.siegel.q-expansion
Fourier expansion smf
mf.bianchi.fourierbessell
Fourier-Bessel expansion
st_group.fourth_trace_moment
Fourth trace moment
ring.fractional_ideal
Fractional ideal
group.frattini_subgroup
Frattini subgroup of a group
ec.q.frey
Frey curve
cmf.fricke
Fricke involution
av.fq.frobenius_angles
Frobenius angles
nf.frobenius_cycle_types
Frobenius cycle types
modlgal.frobenius_matrix
Frobenius matrix
av.fq.frobenius_order
Frobenius Order
modlgal.frobenius_order
Frobenius order
modlgal.frobenius_prime
Frobenius prime
modlgal.frobenius_trace
Frobenius trace
artin.frobenius_schur_indicator
Frobenius-Schur indicator of a representation
group.fuchsian
Fuchsian group
curve.highergenus.aut.full
Full group of automorphisms
av.fq.class_number_1
Function fields of class number 1
lfunction.functional_equation
Functional equation of an L-function
group.fuchsian.fundamental_domain
Fundamental domain
group.sl2z.fundamental_domain
Fundamental domain of $\SL(2,\Z)$
nf.fundamental_units
Fundamental units of a number field
dq.av.fq.further_extent
Further extent of the data on isogeny classes of abelian varieties over finite fields
G
g2c.g2_invariants
G2-invariants of a genus 2 curve
nf.galois_closure
Galois closure of an extension
cmf.galois_conjugate
Galois conjugate newforms
gg.galois_group
Galois group
nf.galois_group
Galois group
nf.galois_search
Galois group
nf.galois_group.data
Galois group information
gg.label
Galois group label
nf.galois_group.name
Galois group of a number field -- naming convention
av.fq.galois_group
Galois group of an isogeny class of abelian varieties
lf.galois_invariants
Galois invariants of a local field
lf.galois_mean_slope
Galois mean slope
nf.galois_group.gmodule
Galois module information
nf.galois_group.gmodule_v4_type_i_i
Galois module structure of Type I (i) for units in biquadratic number fields
nf.galois_group.gmodule_v4_type_i_ii
Galois module structure of Type I (ii) for units in biquadratic number fields
nf.galois_group.gmodule_v4_type_i_iii
Galois module structure of Type I (iii) for units in biquadratic number fields
nf.galois_group.gmodule_v4_type_ii_i
Galois module structure of Type II (i) for units in biquadratic number fields
nf.galois_group.gmodule_v4_type_ii_ii
Galois module structure of Type II (ii) for units in biquadratic number fields
nf.galois_group.gmodule_v4_type_iii
Galois module structure of Type III for units in biquadratic number fields
nf.galois_group.gmodule_v4_type_iv
Galois module structure of Type IV for units in biquadratic number fields
mf.siegel.galois_orbit
Galois orbit
cmf.hecke_galois_orbit
Galois orbit label
character.dirichlet.galois_orbit
Galois orbit of a Dirichlet character
cmf.galois_orbit
Galois orbit of a newform
artin.galois_orbit
Galois orbit of an Artin representation
cmf.galois_representation
Galois representation
ec.galois_rep
Galois representations attached to an elliptic curve
g2c.galois_rep
Galois representations attached to the Jacobian of a genus 2 curve
nf.galois_root_discriminant
Galois root discriminant
lf.galois_splitting_model
Galois splitting model of a local field
lfunction.gamma_factor
Gamma factors
modcurve.gassmann_class
Gassmann class
group.gassmann_equivalence
Gassmann equivalence
character.dirichlet.gauss_sum
Gauss sum
group.generalized_quaternion
Generalized quaternion
lfunction.rh
Generalized Riemann hypothesis
group.pseudo_random_elements
Generating deterministic sequences of pseudo-random group elements
modlgal.generating_primes
Generating Frobenius classes
curve.highergenus.aut.generatingvector
Generating Vector
nf.field_generator
Generator of a number field
nf.generator
Generator of a number field
character.dirichlet.group.generators
Generators of a Dirichlet character group
group.generators
Generators of a group
st_group.generators
Generators of a Sato-Tate group
group.permutation_gens
Generators of permutation group
lmfdb.object_information
Generic dynamic knowl
g2c.g2curve
Genus 2 curve
belyi.genus
Genus of a Belyi map
modcurve.genus
Genus of a modular curve
shimcurve.genus
Genus of a Shimura curve
ag.curve.genus
Genus of a smooth curve
gl2.genus
Genus of a subgroup of $\GL_2$
group.sl2z.genus_subgroup
Genus of a subgroup of the modular group
lattice.genus
Genus of an integral lattice
modcurve.genus_minus_rank
Genus-rank difference
g2c.geom_aut_grp
Geometric automorphism group
ag.geom_component
Geometric component
modcurve.components
Geometric components of a modular curve
ag.geom_endomorphism_algebra
Geometric endomorphism algebra
g2c.geom_end_alg
Geometric endomorphism algebra
ag.geom_endomorphism_ring
Geometric endomorphism ring
ec.geom_endomorphism_ring
Geometric endomorphism ring
ag.gonality_geom
Geometric gonality
g2c.geometric_invariants
Geometric invariants
g2c.geom_iso_class
Geometric isomorphism class of a curve
ag.geom_simple
Geometrically simple
av.geometrically_simple
Geometrically simple
av.geometrically_squarefree
Geometrically squarefree abelian variety
belyi.geometry_type
Geometry type of a Belyi map
gl2.subgroup_data
GL2 subgroup data
g2c.gl2type
$\GL_2$-type
ec.global_minimal_model
Global minimal model
ec.period
Global period of an elliptic curve
ag.gonality
Gonality of a curve
ag.good_reduction
Good and bad reduction
ec.good_ordinary_reduction
Good ordinary reduction
ec.good_reduction
Good reduction
ec.good_supersingular_reduction
Good supersingular reduction
lattice.gram
Gram matrix
mf.siegel.lift.gritsenko
Gritsenko lift
gg.group_action_invariants
Group action Invariants
curve.highergenus.aut.groupalgebradecomp
Group algebra decomposition of Jacobian varieties
mf.sl2.subgroup.gamma0n
Group $\Gamma_0(N)$ subgroup of $\textrm{SL}(2,\mathbb{Z})$
mf.sl2.subgroup.gamma1n
Group $\Gamma_1(N)$ subgroup of $\textrm{SL}(2,\mathbb{Z})$
group.homomorphism
Group homomorphism
gg.invariants
Group invariants
group.isomorphism
Group isomorphism
lattice.group_order
Group order of an integral lattice
group.group_ring
group ring
group.about
Groups
mf.growth_condition
Growth condition for a modular form
gsp4.subgroup_data
GSp4 subgroup data
doc.knowl.annotation_guidelines
Guidelines for writing annotations
H
group.haar_measure
Haar measure of a topological group
mf.half_integral_weight
Half-integral weight modular forms
group.subgroup.hall
Hall subgroup
g2c.has_square_sha
Has square Ш
combin.hasse_diagram
Hasse diagram
g2c.hasse_weil_conjecture
Hasse-Weil conjecture
lfunction.history.hasse_weil
Hasse-Weil L-function
hecke_algebra.definition
Hecke algebra
mf.bianchi.hecke_algebra
Hecke algebra
character.hecke
Hecke character
cmf.heckecharpolys
Hecke characteristic polynomial
mf.gl2.history.hecke
Hecke Characters
mf.hilbert.eigenvalue
Hecke eigenvalues
cmf.hecke_kernels
Hecke kernel
lfunction.history.hecke_characters
Hecke L-functions
cmf.hecke_operator
Hecke operator
mf.siegel.hecke_operator
Hecke operators
lfunction.history.hecke_operators
Hecke operators, history
cmf.hecke_orbit
Hecke orbit
mf.hilbert.hecke_orbit
Hecke orbit for Hilbert modular form
lattice.hermite_number
Hermite number
crystals.highest_weight
Highest weight crystals
repn.highest.weight
Highest weight of an irreducible representation of $\GL(g,\C)$.
mf.hilbert
Hilbert modular form
nf.ideal.label.hmf
Hilbert modular form convention for the label of a number field ideal
hmsurface.hmsurface
Hilbert modular surface
rcs.source.hmsurface
Hilbert modular surfaces source
lattice.history
History of Lattices
st_group.hodge_circle
Hodge circle
hmsurface.hodge_numbers
Hodge numbers
hgm.hodge_vector
Hodge vector of a hypergeometric motive
mot.hodgevector
Hodge vector of a hypergeometric motive
cmf.eisenstein
Holomorphic Eisenstein series of level 1
ag.holomorphic_euler_char
Holomorphic Euler characteristic
av.fq.honda_tate
Honda-Tate theorem
rcs.cite.av.fq
How to cite abelian varieties over finite fields
rcs.cite.groups.abstract
How to cite abstract groups
rcs.cite.artin
How to cite Artin representations
rcs.cite.belyi
How to cite Belyi maps
rcs.cite.mf.bianchi
How to cite Bianchi modular forms
rcs.cite.cmf
How to cite classical modular forms
rcs.cite.curve.highergenus.aut
How to cite curves of higher genus with automorphism group data
rcs.cite.character.dirichlet
How to cite Dirichlet characters
rcs.cite.ec.q
How to cite elliptic curves over $\mathbb{Q}$
rcs.cite.ec
How to cite elliptic curves over number fields
rcs.cite.gg
How to cite Galois groups
rcs.cite.g2c
How to cite genus 2 curves
rcs.cite.mf.hilbert
How to cite Hilbert modular forms
rcs.cite.hgm
How to cite hypergeometric motive data
rcs.cite.lfunction
How to cite L-functions
rcs.cite.maass
How to cite Maass forms
rcs.cite.nf
How to cite number fields
rcs.cite.lf
How to cite p-adic fields
rcs.cite.st_group
How to cite Sato-Tate groups
content.how_to_cite
How to cite the LMFDB
dq.zeros.zeta.howcomputed
How zeros of the Riemann zeta function were computed
curve.highergenus.hurwitz_bound
Hurwitz bound
mf.bianchi.hyperbolic3space
Hyperbolic 3-space
group.hyperelementary
Hyperelementary group
ag.hyperelliptic_curve
Hyperelliptic curve
hgm.familes
Hypergeometric family over $\Q$
hgm.motive
Hypergeometric motive
I
nf.ideal_class_group
Ideal class group of a number field
nf.ideal_labels
Ideal labels
ring.ideal
Ideal of a ring
doc.knowl.identifier
Identifier of a knowl
st_group.identity_component
Identity component of a Sato-Tate group
alg.binary_operation.identity
Identity for a binary operation
g2c.igusa_invariants
Igusa invariants of a genus 2 curve
g2c.igusa_clebsch_invariants
Igusa-Clebsch invariants of a genus 2 curve
modlgal.image
Image
group.representation.image
Image of a representation
ec.galois_rep_elladic_image
Image of $\ell$-adic Galois representation
g2c.galois_rep_image
Image of mod p Galois Representation of Jacobian of genus 2 curve
ec.galois_rep_modell_image
Image of mod-$\ell$ Galois representation
ec.galois_rep_adelic_image
Image of the adelic Galois representation
artin.gg_quotient
Image of the representation
doc.knowl.implicit
Implicit creation of knowls
hgm.imprimitivity_index
Imprimitivity index of a hypergeometric motive
hgm.rotation_number
Imprimitivity index of a hypergeometric motive
cmf.include_all_spaces
Include all spaces
gg.int_modules
Indecomposable integral representation
modcurve.index
Index of a modular curve
modcurve.relative_index
Index of a modular map
nf.zk_index
Index of a number field
shimcurve.index
Index of a Shimura curve
group.subgroup.index
Index of a subgroup
gl2.index
Index of an open subgroup
nf.index
Index of an order
av.fq.zfv_index
Index of maximal order
av.fq.zfv_real_index
Index of Real Order
st_group.index
Index of the identity component
modlgal.image_index
Index of the image of a mod-$\ell$ Galois representation
intro.description
Index page, first sentences
lf.indices_of_inseparability
Indices of inseparability
character.dirichlet.induce
Induced Dirichlet character
lf.inertia_group
Inertia group
lf.inertia_group_search
Inertia group searching
nf.inessential_prime
Inessential prime
mf.gl2.history.infinite
Infinite products
lfunction.infinity_factor
Infinity factor of an L-function
users.jhs.note
Information about Joe Silverman
av.fq.initial_coefficients
Initial coefficients of the L-polynomial
group.inner_automorphism
Inner automorphism of a group
cmf.inner_twist
Inner twist
cmf.inner_twist_count
Inner twist count
cmf.inner_twist_group
Inner twist group
cmf.inner_twist_multiplicity
Inner twist multiplicity
cmf.inner_twist_proved
Inner twist proved
gg.arithmetically_equiv_input
Input for arithmetically equivalent fields
nf.integral_basis
Integral basis of a number field
ring.integral_domain
Integral domain
ring.integral
Integral element of a ring
nf.integral
Integral elements
lattice.definition
Integral Lattice
ec.integral_model
Integral model
ec.q.integral_points
Integral points
ring.integrally_closed
Integrally closed
group.properties_interdependencies
Interdependencies of group properties
group.subgroup_properties_interdependencies
Interdependencies of subgroup properties
lf.intermediate_fields
Intermediate fields
nf.intermediate_fields
Intermediate fields
intro
Introduction
intro.features
Introduction/Features
g2c.invariants
Invariants of a genus 2 curve
modcurve.invariants
Invariants of a modular curve
shimcurve.invariants
Invariants of a Shimura curve
lfunction.invariants
Invariants of an L-function
alg.binary_operation.inverse
Inverse for a binary operation
ring.irreducible
Irreducible element
repn.irrep.gl
Irreducible representations of $\GL(g,\C)$
ag.irreducible
Irreducible variety
nf.is_galois
Is a Galois extension
group.isoclinism
Isoclinism
ec.isogeny
Isogeny between elliptic curves
av.fq.abvar.data
Isogeny class data
ec.isogeny_class_degree
Isogeny class degree
av.isogeny_class
Isogeny class of an abelian variety
g2c.isogeny_class
Isogeny class of an abelian variety
ec.isogeny_class
Isogeny class of an elliptic curve
modcurve.decomposition
Isogeny decomposition of the Jacobian of a modular curve
ec.isogenygraph.legend
Isogeny graph legend
ec.isogeny_graph
Isogeny graph of an isogeny class of elliptic curves
ec.isogeny_matrix
Isogeny matrix of an isogeny class of elliptic curves
av.isogeny
Isogeny of abelian varieties
nf.isogeny_primes
Isogeny primes of elliptic curves
ag.isolated_point
Isolated point
modcurve.isolated_point
Isolated point on a modular curve
lattice.isometry
Isometries between integral lattices
ec.weierstrass_isomorphism
Isomorphism between Weierstrass models
av.fq.isogeny_class_size
Isomorphism classes within an isogeny class
ec.isomorphism
Isomorphism of elliptic curves
ec.iwasawa_invariants
Iwasawa invariants of elliptic curves
J
ec.j_invariant_denominator_valuation
j-invariant denominator valuation
modcurve.j_invariant_map
$j$-invariant map
ec.q.j_invariant
j-invariant of a rational elliptic curve
ec.j_invariant
j-invariant of an elliptic curve
mf.jacobi
Jacobi forms
character.dirichlet.jacobi_sum
Jacobi sum
character.dirichlet.jacobi_symbol
Jacobi symbol
ag.jacobian
Jacobian of a curve
av.fq.jacobian
Jacobian of a curve
g2c.jacobian
Jacobian of a genus 2 curve
lf.jump_set
Jump set
K
specialfunction.k_bessel
$K$-Bessel functions
modcurve.gonality
$K$-gonality of a modular curve
shimcurve.gonality
$K$-gonality of a Shimura curve
group.representation.kernel
Kernel of a character
lattice.kissing
Kissing number
character.dirichlet.kloosterman_sum
Kloosterman sum
doc.knowl
Knowl
doc.knowl.guidelines
Knowl Edit Guidelines
test.knowlparam
Knowl with parameters
modcurve.known_points
Known points
g2c.known_rational_points
Known rational points
ag.kodaira_dimension
Kodaira dimension
hmsurface.kodaira_dimension
Kodaira dimension
ec.kodaira_symbol
Kodaira symbol
ec.q.kodaira_symbol
Kodaira symbol
mf.siegel.koecher.principle
Koecher principle
character.dirichlet.kronecker_symbol
Kronecker symbol
L
lfunction
L-function
cmf.lfunction
L-function of a classical modular form
g2c.lfunction
L-function of an abelian variety over $\mathbb{Q}$
lfunction.spectral_parameters
L-function spectral parameters
lfunction.history.maass
L-functions of Maass forms
av.fq.l-polynomial
L-polynomial of an abelian variety
lf.field.label
Label for a $p$-adic field
artin.label
Label for an Artin representation
ec.q.lmfdb_label
Label for an elliptic curve over $\mathbb Q$
cmf.label
Label of a classical modular form
group.label_conjugacy_class
Label of a conjugacy class
character.dirichlet.galois_orbit_label
Label of a Galois orbit of a Dirichlet character
g2c.label
Label of a genus 2 curve over $\Q$
group.label
Label of a group
hmsurface.label
Label of a Hilbert modular surface
hgm.field.label
Label of a hypergeometric motive
mf.maass.label
Label of a Maass newform
modcurve.label
Label of a modular curve
mf.siegel.label
Label of a Siegel modular form
gl2.label
Label of a subgroup $\GL_2(\widehat\mathbb Z)$
mf.hilbert.label
Label of an Hilbert Modular Form
group.label_complex_group_char
Label of irreducible complex characters of groups
lfunction.label
Label of L-function
group.label_rational_group_char
Label of rational character of a group
modcurve.search_input
Label search
dq.curve.highergenus.aut.label
Labeling convention for families of higher genus curves
character.dirichlet.conrey.orbit_label
Labels for Galois orbits of Dirichlet Characters
av.fq.lmfdb_label
Labels for isogeny classes of abelian varieties over finite fields
group.small_group_label
Labels for the small group database in GAP and Magma
mf.bianchi.labels
Labels of Bianchi modular forms
ec.curve_label
Labels of elliptic curves over number fields
modlgal.label
Labels of mod-$\ell$ Galois representations
ec.lambda_invariant
lambda-invariant of an elliptic curve
lfunction.history.langlands_program
Langlands program
mf.maass.mwf.laplacian
Laplace-Beltrami operator (hyperbolic)
mf.maass.picard.laplacian
Laplacian in 3d hyperbolic upper half-space
doc.macros
LaTeX macros in the LMFDB
rcs.ack.lattice
Lattice additional acknowledgments
lfunction.leading_coeff
Leading coefficient
lfunction.degree2holo.key
Legend for GL(2) holomorphic graph of dots
character.dirichlet.legendre_symbol
Legendre symbol
hmsurface.levelnorm
Level norm
mf.bianchi.level
Level of a Bianchi modular form
mf.hilbert.level_norm
Level of a Hilbert modular form
modcurve.level
Level of a modular curve
cmf.level
Level of a modular form
sh.level
Level of a Shimura curve
shimcurve.level
Level of a Shimura curve
mf.siegel.level
Level of a Siegel modular form
lattice.level
Level of an integral lattice
gl2.level
Level of an open subgroup
modcurve.level_structure
Level structure of a modular curve
hgm.levelt_matrices
Levelt matrices of a hypergeometric family
mf.siegel.lift
Lift Siegel modular form
group.linear
Linear and Projective Linear Groups
crystals.littelmann_path
Littelmann path model for crystals
doc.lmfdb.improve
LMFDB backend
lattice.label
LMFDB label of an integral lattice
doc.news.in_the_news
LMFDB Press
lf.algebra.data
Local algebra
nf.local_algebra
Local algebra
ec.local_data
Local data of an elliptic curve
lf.local_field
Local field
lf.invariants
Local field invariants
g2c.local_invariants
Local invariants
g2c.good_lfactors
Local L-factors at good primes
ec.local_minimal_discriminant
Local minimal discriminant of an elliptic curve
ec.local_minimal_model
Local minimal model
modcurve.local_obstruction
Local obstruction
ec.local_root_number
Local root number
g2c.locally_solvable
Locally solvable
group.lower_central_series
Lower central series of a group
lucant
LuCaNT Conference
M
mf.maass.mwf.coefficients
Maass form coefficients
mf.maass.mwf
Maass form on GL2(R) with trivial character
mf.maass.mwf.plot
Maass form plot
mf.maass.mwf.weight0
Maass forms of weight 0
mf.maass
Maass forms on GL(n)
mf.maass.picard
Maass forms on PSL(2,Z[i])
mf.siegel.lift.maass
Maass lift from Jacobi form to Siegel modular form
content.edit_board
Management board
ec.q.manin_constant
Manin constant for elliptic curves over $\Q$
ec.q_curve
$\mathbb{Q}$-curves
group.matrix_group
Matrix group
group.division_maximal
Maximal division of a group
ec.maximal_elladic_galois_rep
Maximal $\ell$-adic Galois representation
av.fq.maximal_zfv
Maximal Frobenius order
ec.maximal_galois_rep
Maximal Galois representation
ring.maximal_ideal
Maximal ideal
lf.maximal_ideal
Maximal ideal of a local field
cmf.maximal
Maximal newform
group.maximal_quotient
Maximal quotient of a group
group.maximal_subgroup
Maximal subgroup of a group
st_group.subgroups
Maximal subgroups
group.metabelian
Metabelian group
group.metacyclic
Metacyclic group
group.min_complex_irrep_deg
Minimal degree of a complex irrep
group.min_complex_rep_deg
Minimal degree of a complex representation
group.min_rational_irrep_deg
Minimal degree of a rational irrep
group.min_rational_rep_deg
Minimal degree of a rational representation
character.dirichlet.minimal
Minimal Dirichlet character
ec.minimal_discriminant
Minimal discriminant
g2c.minimal_equation
Minimal equation of a hyperelliptic curve
group.min_faithful_linear
Minimal faithful linear representations
ag.minimal_field
Minimal field of definition
cmf.minimal
Minimal modular form
group.minimal_normal
Minimal normal subgroup
nf.minimal_polynomial
Minimal polynomial
nf.minimal_sibling
Minimal sibling
st_group.supgroups
Minimal supergroups
ec.q.minimal_twist
Minimal twists of elliptic curves over $\mathbb{Q}$
lattice.minimal_vector
Minimal vector length
ec.q.minimal_weierstrass_equation
Minimal Weierstrass equation over $\mathbb Q$
group.representation.min_perm_rep
Minimum permutation representation
cmf.minus_space
Minus space
mf.siegel.lift.miyawaki
Miyawaki lift
mf.siegel.lift.miyawaki1
Miyawaki lift of type I, Ikeda-Miyawaki lift
mf.siegel.lift.miyawaki2
Miyawaki lift of type II
g2c.galois_rep_modell_image
Mod-$\ell$ Galois image of a genus 2 curve
modlgal
Mod-$\ell$ Galois representation
upload.multi_knowl
modcurve.ref.gonalities
upload.modcurve.name_or_label
modcurve.ref.sporadic
modcurve.modular_cover
Modular cover
modcurve
Modular curve
modcurve.model
Modular curve models
modcurve.xn
Modular curve $X(N)$
ag.modcurve.x0
Modular curve $X_0(N)$
ag.modcurve.x1
Modular curve $X_1(N)$
ag.modcurve.xnsp
Modular curve $X_{\text{ns}}^{+}(N)$
ec.q.modular_degree
Modular degree of an elliptic curve over $\mathbb Q$
mf
Modular form (general)
ec.q.modular_form
Modular form associated to an elliptic curve/$\mathbb Q$
mf.about
Modular Forms
group.sl2z
Modular group $\mathrm {SL}(2,\mathbb Z)$
ec.q.modular_parametrization
Modular parametrization of an elliptic curve over $\mathbb Q$
character.dirichlet.modulus
Modulus of a Dirichlet character
st_group.moment_matrix
Moment matrix
st_group.moment_simplex
Moment simplex
st_group.moments
Moment statistics
curve.highergenus.aut.monodromy
Monodromy Group
belyi.group
Monodromy group of a Belyi map
hgm.monodromy
Monodromy group of a hypergeometric family
nf.monogenic
Monogenic field
group.monomial
Monomial group
nf.monomial_order
Monomial order
g2c.mw_generator
Mordell-Weil generator
ec.mw_generators
Mordell-Weil generators
ec.mordell_weil_group
Mordell-Weil group
ag.mordell_weil
Mordell-Weil group of an abelian variety
g2c.mordell_weil_rank
Mordell-Weil rank
ec.mordell_weil_theorem
Mordell-Weil theorem
motives.about
Motives
lfunction.motivic_weight
Motivic weight
ec.mu_invariant
mu-invariant of an elliptic curve
af.multiplicative
Multiplicative arithmetic function
nf.multiplicative_gal_module
Multiplicative Galois Module Structure
ec.multiplicative_reduction
Multiplicative reduction
mf.maass.mwf.dimension
Multiplicity of an eigenvalue
mf.multipliersystem
Multiplier system
group.mobius_function
Möbius function of subgroup lattice
N
lattice.name
Name of a lattice
st_group.name
Name of a Sato-Tate group
doc.knowl.naming_conventions
Naming conventions for knowls
doc.knowl.naming_suggestions
Naming suggestions
nf.narrow_class_group
Narrow class group
nf.narrow_class_number
Narrow class number
mf.gl2.history.new
New modular forms from given ones
cmf.newspace
New subspace
cmf.newform
Newform
modcurve.newform_level
Newform level of a modular form
cmf.newform_subspace
Newform subspace
mf.siegel.newform_subspace
Newform subspace
lf.newton_polygon
Newton polygon of a polynomial
group.nilpotent
Nilpotent group
cmf.nk2
Nk^2
ring.noetherian
Noetherian ring
modcurve.nonrational_point
Non rational low degree point
ag.singular_point
Non-singular point (definition)
gl2.nonsplit_cartan
Non-split Cartan subgroup
ec.nonsplit_multiplicative_reduction
Non-split multiplicative reduction
g2c.galois_rep.non_maximal_primes
Nonmaximal primes associated to genus $2$ curve
cmf.nontrivial_twist
Nontrivial inner twist
ec.discriminant_norm
Norm of discriminant
group.subgroup.normal_closure
Normal closure of a subgroup
group.normal_series
Normal series of a group
group.subgroup.normal
Normal subgroup of a group
lfunction.normalization
Normalization of an L-function
nf.defining_polynomial.normalization
Normalization of defining polynomials for number fields
lattice.normalized_minimal_vector
Normalized minimal vector of a lattice
gl2.normalizer_cartan
Normalizer of a Cartan subgroup
gl2.normalizer_nonsplit_cartan
Normalizer of a non-split Cartan subgroup
gl2.normalizer_split_cartan
Normalizer of a split Cartan subgroup
group.subgroup.normalizer
Normalizer of a subgroup
nf
Number field
artin.number_field
Number field associated to an Artin representation
nf.field.link
Number field defined by polynomial
nf.invariants
Number field invariants
nf.label
Number field label
nf.nickname
Number field nicknames
nf.field.missing
Number field not in the database
av.fq.number_field
Number field of an isogeny class of abelian varieties
nf.elkies
Number fields contributed by Noam Elkies
character.dirichlet.related_fields
Number fields related to a Dirichlet character
belyi.num_orbits
Number of Galois orbits
av.hyperelliptic_count
Number of hyperelliptic Jacobians
av.jacobian_count
Number of Jacobians
modcurve.models
Number of models
g2c.num_rat_pts
Number of rational points
O
ec.obstruction_class
Obstruction class of an elliptic curve
cmf.oldspace
Old subspace of modular forms
cmf.decomposition.old.gamma1
Oldspace decomposition for Gamma1(N)
cmf.decomposition.old.gamma0chi
Oldspace decomposition for newform space
gl2.open
Open subgroup
ec.q.optimal
Optimal elliptic curve over $\mathbb Q$
character.dirichlet.galois_orbit_index
Orbit index of a Dirichlet character
belyi.orbit_size
Orbit size
nf.order
Order
character.dirichlet.order
Order of a Dirichlet character
character.dirichlet.conrey.order
Order of a Dirichlet character from its label
character.dirichlet.group.order
Order of a Dirichlet character group
group.order
Order of a group
group.element_order
Order of a group element
g2c.mw_generator_order
Order of a Mordell-Weil generator
group.order_conjugacy_class
Order of elements in a conjugacy class
modlgal.image_order
Order of the image of a mod-$\ell$ Galois representation
group.order_stats
Order statistics of a group
av.fq.ordinary
Ordinary
modcurve.other_labels
Other labels for modular curves
group.outer_aut
Outer automorphism group
group.over_subgroup
Over-subgroup
P
nf.padic_completion
$p$-adic completion of a number field
lf.padic_field
$p$-adic field
lf
$p$-adic field (local number field)
lf.log
$p$-adic logarithm
group.pgroup
$p$-group
hgm.defining_parameter_ppart
p-part of defining parameters of a hypergeometric motive
av.fq.p_rank
p-rank
g2c.paramodular_conjecture
Paramodular conjecture
group.paramodular
Paramodular group
paramodulargroup.sp2gr
Paramodular group in degree g
mf.siegel.newform.paramodular
Paramodular newform
character.dirichlet.parity
Parity of a Dirichlet character
character.dirichlet.conrey.parity
Parity of a Dirichlet character from its Conrey label
gg.parity
Parity of a Galois group
artin.parity
Parity of a representation
belyi.passport
Passport
belyi.passport_label
Passport label
belyi.pass_size
Passport size of a Belyi map
group.perfect
Perfect groups
ec.q.period_lattice
Period lattice of an elliptic curve
group.permutation_degree
Permutation degree
group.permutation_module
permutation module
group.permutation_representation
Permutation representation
cmf.petersson_scalar_product
Petersson scalar product
cmf.picture_description
Pictures for classical modular forms
portrait.cmf
Pictures for classical modular forms
portrait.ec.q
Pictures for elliptic curves over $\mathbb{Q}$
portrait.maass
Pictures for Maass forms
portrait.modcurve
Pictures of modular curves
nf.place
Place of a number field
ag.plane_model
Plane model
modcurve.plane_model
Plane model
cmf.plus_space
Plus space
mf.gl2.history.poincare
Poincaré series
specialfunction.poincare
Poincaré series
ag.fq.point_counts
Point counts of a variety
av.fq.curve_point_counts
Point counts of the curve
av.polarization
Polarization
shimcurve.nrdmu
Polarization degree of a polarized order
hmsurface.polarization_module
polarization module
shimcurve.polarized_order
Polarized quaternion order
lattice.postive_definite
Positive definite lattice
ag.potential_good_reduction
Potential good reduction
ec.potential_good_reduction
Potential good reduction
av.potential_toric_rank
Potential toric rank
group.conjugacy_class.power_classes
Power classes
dq.cmf.cc_prec
Precision of classical modular form eigenvalues
group.presentation
Presentation of a finite group
doc.lmfdb.contextualize
Presentation of the data in the LMFDB
group.primary_decomposition
Primary decomposition of abelian group
ring.prime_ideal
Prime ideal
nf.prime
Prime of a number field
ag.bad_prime
Prime of bad reduction
hgm.defining_parameter_primetoppart
prime to $p$-part of defining parameters of a hypergeometric motive
hgm.good_prime
Primes of good and bad reduction of a hypergeometric motive
g2c.good_reduction
Primes of good reduction
ag.primitive
Primitive algebraic variety
belyi.primitive
Primitive Belyi map
character.dirichlet.primitive
Primitive Dirichlet character
nf.primitive_element
Primitive element
lattice.primitive
Primitive integral lattice
lfunction.primitive
Primitive L-function
gg.primitive
Primitivity of a Galois group
belyi.primitivization
Primitivization of a Belyi map
character.dirichlet.principal
Principal Dirichlet character
ring.principal_fractional_ideal
Principal fractional ideal
ag.torsor
Principal homogeneous space
ring.principal_ideal_domain
Principal ideal domain
av.princ_polarizable
Principally polarizable
gl2.profinite
Profinite group
artin.projective_field
Projective Artin field
cmf.projective_field
Projective field
cmf.projective_image
Projective image
group.subgroup.projective_image
Projective image of a subgroup
artin.projective_image
Projective image of an Artin representation
artin.projective_image_type
Projective image type
ag.projective_space
Projective space
group.psl2r
Projective special linear group $\text{PSL}_2(\mathbb{R})$
artin.projective_stem_field
Projective stem field of an Artin representation
group.proper_subgroup
Proper subgroup
stats.proportions
Proportions for statistics
modcurve.psl2index
$\PSL_2$-index
Q
mf.hilbert.q_expansion
q-expansion of a Hilbert modular form
cmf.q-expansion
q-expansion of a modular form
modcurve.quadratic_refinements
Quadratic refinements
mf.quasi_modular
Quasi-modular form
group.quasisimple
Quasisimple group
shimcurve.quaternion_algebra
Quaternion algebra
shimcurve.order
Quaternion order
ag.quotient_curve
Quotient curve
curve.highergenus.aut.quotientgenus
Quotient genus
group.quotient
Quotient group
group.quotient_isolabel
Quotient label
R
group.radical
Radical of a group
lfunction.history.ramanujan_tau
Ramanujan tau L-function
lf.ramification_index
Ramification index of a prime in a local field
lf.ramification_polygon
Ramification polygon
lf.ramification_polygon_display
Ramification polygon
belyi.ramification_type
Ramification type
nf.ramified_primes
Ramified (rational) prime of a number field
artin.ramified_primes
Ramified prime of an Artin representation
modlgal.ramified
Ramified primes of a mod-$\ell$ Galois representation
group.rank
Rank
nf.rank
Rank of a number field
ec.rank
Rank of an elliptic curve over a number field
lfunction.history.rankin_selberg
Ranking-Selberg convolution, history
group.representation.rational_character
Rational character
group.rational_character_table
Rational character table of a group
group.rational_group
Rational group
lfunction.rational
Rational L-function
g2c.all_rational_points
Rational points
modcurve.rational_points
Rational points on a modular curve
st_group.rational
Rational Sato-Tate group
st_group.real_dimension
Real dimension of a Sato-Tate group
character.dirichlet.real
Real Dirichlet character
nf.real_embedding
Real embedding
ag.real_endomorphism_algebra
Real endomorphism algebra
ag.real_geom_endomorphism_algebra
Real geometric endomorphism algebra
ag.real_multiplication
Real multiplication
cmf.rm_form
Real multiplication
ec.q.real_period
Real period
g2c.real_period
Real period
ec.reduction
Reduction of an elliptic curve
ec.reduction_type
Reduction type
ec.q.reduction_type
Reduction type of an elliptic curve over $\mathbb Q$
curve.highergenus.aut.refinedpassport
Refined passport
nf.reflex_field
Reflex field
nf.reflex_reflex_field
Reflex field of the reflex field
g2c.regulator
Regulator of a genus 2 curve
nf.regulator
Regulator of a number field
ag.regulator
Regulator of an abelian variety
ec.regulator
Regulator of an elliptic curve
ec.q.regulator
Regulator of elliptic curve
doc.related_to
Related objects
cmf.relative_dimension
Relative dimension
av.fq.zfv_rel_disc_norm
Relative discriminant norm
rcs.release.1.3
Release notes for version 1.3
rcs.rigor.groups.abstract
Reliability of abstract groups data
rcs.rigor.artin
Reliability of Artin representation data
rcs.rigor.belyi
Reliability of Belyi map data
dq.mf.bianchi.reliability
Reliability of Bianchi Modular Form data
rcs.rigor.mf.bianchi
Reliability of Bianchi modular form data
rcs.rigor.lfunction.curve
Reliability of Curve L-function Data
rcs.rigor.character.dirichlet
Reliability of Dirichlet Character Data
rcs.rigor.lfunction.dirichlet
Reliability of Dirichlet L-function Data
rcs.rigor.lfunction.lcalc
Reliability of Dynamically Computed L-function Data
rcs.rigor.ec
Reliability of elliptic curve data
dq.ecnf.reliability
Reliability of elliptic curve data over number fields
rcs.rigor.ec.q
Reliability of elliptic curve data over $\Q$
rcs.rigor.lfunction.ec
Reliability of Elliptic Curve L-function Data
rcs.rigor.g2c
Reliability of Genus 2 Curve Data
rcs.rigor.nf
Reliability of global number field data
rcs.rigor.mf.hilbert
Reliability of Hilbert modular form data
rcs.rigor.hgm
Reliability of hypergeometric motive data
rcs.rigor.lfunction
Reliability of L-function data
rcs.rigor.lattice
Reliability of lattice data
rcs.rigor.lf
Reliability of local field data
rcs.rigor.lfunction.maass
Reliability of Maass form L-function data
rcs.rigor.maass
Reliability of Maass forms data
rcs.rigor.modlgal
Reliability of mod-$\ell$ Galois representation data
rcs.rigor.modcurve
Reliability of modular curve data
rcs.rigor.lfunction.modular
Reliability of Modular L-function Data
rcs.rigor.zeros.zeta
Reliability of Riemann Zeta Zeros Data
rcs.rigor.maass_rigor
Reliability of rigorous Maass forms data
rcs.rigor.st_group
Reliability of Sato-Tate Group Data
rcs.rigor.mf.siegel
Reliability of Siegel modular form data
rcs.rigor.cmf
Reliability of the Classical Modular Form Data
dq.ec.reliability
Reliability of the elliptic curve data
dq.curve.highergenus.aut.reliability
Reliability of the higher genus curves with automorphisms data
rcs.rigor.curve.highergenus.aut
Reliability of the higher genus curves with automorphisms data
dq.mf.hilbert.reliability
Reliability of the Hilbert modular form data
rcs.rigor.gg
Reliability of transitive group data
rcs.rigor.av.fq
Reliability of Weil polynomial data
mf.gl2.history.remainder
Remainder terms
doc.knowl.rename
Renaming a knowl
repn.about
Representation
group.repr_explain
Representative of a conjugacy class
lf.residual_polynomials
Residual polynomials
lf.residue_field
Residue field
lf.residue_field_degree
Residue field degree of a local field
modcurve.point_residue_field
Residue field of a point on a modular curve
gg.resolvents
Resolvents of a Galois group
ag.riemann_surface
Riemann surface
lfunction.riemann
Riemann zeta-function
lfunction.history.riemanns_memoir
Riemann's memoir
lf.ring_of_integers
Ring of integers of a local field
nf.ring_of_integers
Ring of integers of a number field
character.dirichlet.roadmap
Roadmap for Dirichlet characters
ec.roadmap
Roadmap for elliptic curves
content.roadmap
Roadmap for future areas of LMFBD
mf.hilbert.roadmap
Roadmap for Hilbert modular forms
lfunction.roadmap
Roadmap for L-functions
mf.maass.roadmap
Roadmap for Maass forms
mf.siegel.roadmap
Roadmap for Siegel modular forms
cmf.root
Root
lfunction.root_analytic_conductor
Root analytic conductor
lfunction.root_angle
Root angle of L-function
lfunction.root_angle_input
Root angle of L-function
nf.root_discriminant
Root discriminant of a number field
lattice.root_lattice
Root lattice
lf.root_number
Root number of a local field
artin.root_number
Root number of an Artin representation
ec.rouse_label
Rouse label
S
sage.test
Sage cell knowl
sage.cell
Sage cell server
sage
Sage Mathematical Software System
mf.siegel.lift.saito_kurokawa
Saito-Kurokawa lift
cmf.satake_parameters
Satake parameters
st_group.definition
Sato-Tate group
ag.sato_tate_group
Sato-Tate group (of a motive)
st_group.data
Sato-Tate group data
g2c.st_group_identity_component
Sato-Tate group identity component
st_group.invariants
Sato-Tate group invariants
st_group.label
Sato-Tate group labels
g2c.st_group
Sato-Tate group of a genus 2 curve over Q
cmf.sato_tate
Sato-Tate group of a modular form
st_group.subsupgroups
Sato-Tate subgroups and supergroups
group.representation.schur_index
Schur index
group.schur_multiplier
Schur multiplier
intro.search
Search
doc.search_columns
Search columns
ec.galois_image_search
Searching on Galois images
nf.padic_completion.search
Searching $p$-adic completions of a number field
st_group.second_trace_moment
Second trace moment
lfunction.selberg_class.axioms
Selberg class axioms
lfunction.selberg_class
Selberg class of L-functions
lfunction.selbergdata
Selberg data for the functional equation of an L-function
doc.select_search_columns
Select search columns
cmf.selfdual
Self dual modular form
cmf.self_twist_field
Self twist field
mf.ellitpic.self_twist
Self twist of a modular form
lfunction.self-dual
Self-dual L-function
hmsurface.k2
Self-intersection of canonical divisor
cmf.self_twist
Self-twist
ag.selmer_group
Selmer group of an abelian variety
ec.semi_global_minimal_model
Semi-global minimal model
av.semiabelian_variety
Semiabelian variety
group.semidirect_product
Semidirect product of groups
ec.q.semistable
Semistable elliptic curve
ec.semistable
Semistable elliptic curve
nf.separable_algebra
Separable algebra
nf.separable
Separable extension
nf.serre_odlyzko_bound
Serre Odlyzko bound
cmf.shimura_correspondence
Shimura correspondence
shimcurve
Shimura curve
mf.half_integral_weight.shimura_decomposition
Shimura decomposition
ag.shimura_variety
Shimura variety
nf.sibling
Sibling fields and algebras
gg.other_representations
Siblings for a Galois group
mf.siegel.cusp_form
Siegel cusp form
mf.siegel.cusp_form_degree2
Siegel cusp form of degree 2
mf.siegel.eisenstein_series
Siegel Eisenstein series
mf.siegel.klingen_eisenstein_series
Siegel Klingen-Eisenstein series
mf.siegel
Siegel modular form
mf.siegel.character
Siegel modular form with character
lfunction.history.siegel
Siegel modular forms, history
mf.siegel.newform
Siegel newform
mf.siegel.phi
Siegel $\Phi$ operator
mf.siegel.slash.op
Siegel slash operator
mf.siegel.theta_series
Siegel theta series and theta series with pluriharmonics
mf.siegel.halfspace
Siegel upper half-space
mf.bianchi.sign
Sign of a Bianchi newform
lfunction.root_number
Sign of an L-function
lfunction.sign
Sign of the functional equation
curve.highergenus.aut.signature
Signature of a group action on a curve
nf.signature
Signature of a number field
lfunction.signature
Signature of an L-function
ag.simple
Simple
av.simple
Simple abelian variety
gg.simple_name
Simple group name
group.simple
Simple groups
modcurve.simple
Simple modular curve
ec.simple_equation
Simplified equation
g2c.simple_equation
Simplified equation
group.size_conjugacy_class
Size of a conjugacy class.
group.quotient_size
Size of a quotient
modcurve.sl2level
$\SL_2$-level
lf.slope_content
Slope content of a $p$-adic field
lf.newton_slopes
Slopes of the Newton polygon of a polynomial
group.division_small_large
Small and large divisions of a group
ag.curve.smooth
Smoothness of an algebraic curve
group.socle
Socle of a group
modlgal.solvable
Solvable
group.solvable
Solvable group
cmf.sort_order
Sort order
group.sort_order
Sort order for groups
rcs.source.groups.abstract
Source of abstract group data
rcs.groups.abstract.source
Source of abstract group data
rcs.source.artin
Source of Artin representation data
dq.belyi.source
Source of Belyi maps data
rcs.source.belyi
Source of Belyi maps data
dq.mf.bianchi.source
Source of Bianchi modular form data
rcs.source.mf.bianchi
Source of Bianchi modular form data
rcs.source.cmf
Source of Classical Modular Forms Data
rcs.source.character.dirichlet
Source of Dirichlet character data
rcs.source.lfunction.dirichlet
Source of Dirichlet L-function Data
rcs.source.lfunction.lcalc
Source of Dynamically Computed L-function Data
rcs.source.ec
Source of elliptic curve data
dq.ecnf.source
Source of elliptic curve data over number fields
dq.ec.source
Source of elliptic curve data over $\Q$
rcs.source.ec.q
Source of elliptic curve data over $\Q$
rcs.source.lfunction.ec
Source of Elliptic Curve L-function Data
rcs.source.g2c
Source of Genus 2 Curve Data
rcs.source.nf
Source of global number field data
rcs.source.curve.highergenus.aut
Source of higher genus curves with automorphisms data
dq.mf.hilbert.source
Source of Hilbert modular form data
rcs.source.mf.hilbert
Source of Hilbert modular form data
dq.hgm.source
Source of hypergeometric data
rcs.source.hgm
Source of hypergeometric data
rcs.source.av.fq
Source of isogeny classes of abelian varieties over finite fields
rcs.source.lfunction
Source of L-function data
rcs.source.lfunction.curve
Source of L-function Data
dq.lattice.source
Source of lattice data
rcs.source.lattice
Source of lattice data
rcs.source.lfunction.maass
Source of Maass form L-function Data
rcs.source.maass
Source of Maass forms data
rcs.source.modlgal
Source of mod-$\ell$ Galois representation data
rcs.source.modcurve
Source of modular curve data
rcs.source.lfunction.modular
Source of Modular L-function Data
rcs.source.lf
Source of p-adic field data
rcs.source.zeros.zeta
Source of Riemann Zeta Zeros Data
rcs.source.maass_rigor
Source of rigorous Maass form data
dq.st.source
Source of Sato-Tate group data
rcs.source.st_group
Source of Sato-Tate Group Data
rcs.source.mf.siegel
Source of Siegel modular form data
dq.curve.highergenus.aut.source
Source of the higher genus curves with automorphisms data
rcs.source.gg
Source of transitive group data
rcs
Source, reliability, and completeness
cmf.newspaces
Space of newforms
mf.siegel.newspace
Space of paramodular newforms
mf.bianchi.spaces
Spaces of Bianchi modular forms
cmf.space
Spaces of modular forms
ec.q.special_value
Special value of an elliptic curve L-function
mf.maass.spectral_index
Spectral index of a Maass form
lfunction.spectral_label
Spectral label
mf.maass.picard.eigenvalue
Spectral parameter of Maass forms on PSL(2,Z[i])
group.nonsplit_product
Split and non-split extension of groups
gl2.split_cartan
Split Cartan subgroup
ec.split_multiplicative_reduction
Split multiplicative reduction
ag.splitting_field
Splitting field
modlgal.splitting_field
Splitting field of a mod-$\ell$ Galois representation
av.squarefree
Squarefree abelian variety
curve.highergenus.aut.generators
Standard generators
hmsurface.standard_hmsurfaces
Standard Hilbert modular surfaces
modcurve.name
Standard modular curves
modcurve.standard
Standard modular curves
group.stem_extension
Stem extension
nf.stem_field
Stem field for a Galois extension
group.stem_group
Stem group
character.dirichlet.group.structure
Structure of a Dirichlet group
cmf.sturm_bound
Sturm bound
cmf.sturm_bound_gamma1
Sturm bound for $\Gamma_1(N)$
gg.subfields
Subfields
group.subgroup.diagram
Subgroup diagram
group.subgroup.diagram.lmfdb
Subgroup diagrams in the LMFDB
group.sp2gr.ppal.congruence
Subgroup $\Gamma(N)$ of $\Sp(2g,\Z)$
group.sl2z.subgroup.gamman
Subgroup $\Gamma(N)$ of $\textrm{SL}(2,\mathbb{Z})$
group.sp2gr.gamma0
Subgroup $\Gamma_0(N)$ of $\Sp(2g,\Z)$
group.sl2z.subgroup.gamma0n
Subgroup $\Gamma_0(N)$ of $\textrm{SL}(2,\mathbb{Z})$
group.sp2gr.gamma1
Subgroup $\Gamma_1(N)$ of $\Sp(2g,\Z)$
group.sl2z.subgroup.gamma1n
Subgroup $\Gamma_1(N)$ of $\textrm{SL}(2,\mathbb{Z})$
group.subgroup_isolabel
Subgroup label
group.subgroup_label
Subgroup labels
group.subgroup
Subgroup of a group
group.subgroups_beyond_bound
Subgroups beyond an index bound
gg.subnormal_series
Subnormal series
mf.siegel.subspace.degree.two
Subspaces of degree 2 Siegel modular forms
cmf.subspaces
Subspaces of modular forms
av.fq.supersingular
Supersingular abelian variety
group.supersolvable
Supersolvable group
modlgal.surjective
Surjective
group.sylow_subgroup
Sylow subgroup
group.symmetric
Symmetric group
lfunction.symm
Symmetric power of an L-function
st_group.symplectic_form
Symplectic form
group.sp2gr
Symplectic group
alg.symplectic_isomorphism
Symplectic isomorphism
ec.q.szpiro_ratio
Szpiro ratio
T
gg.tnumber
$T$-number of a transitive group
zeros.first.contents
Table of first zeros of L-function
ec.tamagawa_number
Tamagawa number
g2c.tamagawa
Tamagawa numbers
ec.q.tamagawa_numbers
Tamagawa numbers for an elliptic curve
lf.tame_degree
Tame degree of a local field extension
hgm.tame
Tame primes for hypergeometric families
ec.padic_tate_module
Tate module of an elliptic curve
lfunction.history.tates_thesis
Tate's thesis
ag.tate_shafarevich
Tate-Shafarevich group
lfunction.taxonomy
Taxonomy of L-functions
test.text
test
users.edgarcosta.note
test
test.suggestions
Test knowl suggestions
mf.maass.mwf.eigenvalue
The eigenvalue of a Maass form
mf.maass.mwf.level
The level of a Maass form
hgm.local_discriminant
The local discriminant of a hypergeometric motive
mf.maass.mwf.ncoefficients
The number of coefficients
mf.maass.mwf.precision
The precision of an eigenvalue
mf.siegel.family.kp
The ring of paramodular cusp forms $S_k(K(p))$
mf.siegel.family.gamma_2
The ring of Siegel modular forms of degree 2 for $\Gamma(2)$
mf.siegel.family.gamma0_2
The ring of Siegel modular forms of degree 2 for $\Gamma_0(2)$
mf.siegel.family.gamma0_3
The ring of Siegel modular forms of degree 2 with respect to $\Gamma_0(3)$
mf.siegel.family.gamma0_3_psi_3
The ring of Siegel modular forms of degree 2 with respect to $\Gamma_0(3)$ with character $\psi_3$
mf.siegel.family.gamma0_4
The ring of Siegel modular forms of degree 2 with respect to $\Gamma_0(4)$
mf.siegel.family.gamma0_4_psi_4
The ring of Siegel modular forms of degree 2 with respect to $\Gamma_0(4)$ with character
mf.siegel.family.sp4z
The ring of Siegel modular forms of degree 2 with respect to the full modular group
mf.siegel.family.sp6z
The ring of Siegel modular forms of degree 3 with respect to the full modular group
mf.siegel.family.sp8z
The ring of Siegel modular forms of degree 4 with respect to the full modular group
mf.maass.mwf.spectralparameter
The spectral parameter of a Maass waveform
mf.maass.mwf.symmetry
The symmetry of a Maass form
hgm.type
The type of a hypergeometric motive
lf.unramified_totally_ramified_tower
The unramified/totally ramified tower of a local field
mf.maass.mwf.weight
The weight of a Maass form
mf.siegel.theta_constant
Theta constant
av.theta_divisor
Theta divisor on a principally polarized abelian variety
mf.half_integral_weight.theta
Theta function
mf.gl2.history.theta
Theta functions
lattice.theta
Theta series for an integral lattice
dq.zeros.zeta.toomany
Too many zeros
modlgal.top_slope
Top slope
lf.top_slope
Top slope for a local field
curve.highergenus.aut.topological_equivalence
Topological Equivalence
hmsurface.euler_number
Topological Euler number
group.torsion
Torsion group
ec.q.torsion_growth
Torsion growth in number fields
g2c.torsion_order
Torsion order
ec.torsion_order
Torsion order of an elliptic curve
g2c.torsion
Torsion subgroup
ec.torsion_subgroup
Torsion subgroup of an elliptic curve
ec.q.torsion_subgroup
Torsion subgroup of an elliptic curve over $\mathbb Q$
nf.totally_imaginary
Totally imaginary
nf.totally_positive
Totally positive
nf.totally_real
Totally real
stats.totals
Totals for statistics
cmf.trace_bound
Trace bound
cmf.space_trace_form
Trace form
cmf.trace_form
Trace form
st_group.trace_moments
Trace moments of a Sato-Tate group
artin.trace_of_complex_conj
Trace of complex conjugation
st_group.trace_zero_density
Trace zero density of a Sato-Tate group
doc.knowl.context_free
Transclusion (definition)
mf.transformation_property
Transformation property for modular forms
group.transitive_degree
Transitive degree
gg.conway_name
Transitive group name conventions
belyi.permutation_triple
Transitive permutation triple
group.triangle_group
Triangle group
group.trivial_subgroup
Trivial subgroup
lfunction.trivial_zero
Trivial zeros of an L-function
nf.sextic_twin
Twin sextic algebra
cmf.twist
Twist
cmf.twist_minimal
Twist minimal
cmf.twist_multiplicity
Twist multiplicity
av.twist
Twist of an abelian variety
ec.twists
Twists of elliptic curves
group.representation.type
Type of a complex group representation
group.type
Type of groups
U
group.under_subgroup
Under-subgroup
lfunction.underlying_object
Underlying object of an L-function
character.unit_group
Underlying unit group for a Dirichlet character
lattice.unimodular
Unimodular lattice
ring.unique_factorization_domain
Unique factorization domain
nf.unit_group
Unit group of a number field
nf.torsion
Unit group torsion
ring.unit
Unit in a ring
st_group.usp
Unitary symplectic group
nf.unramified_prime
Unramified (rational) prime of a number field
lf.unramified_degree
Unramified degree of a local field
modlgal.good_prime
Unramified prime
artin.unramified_primes
Unramified prime of an Artin representation
lf.unramified_subfield
Unramified subfield
doc.upload_data
Upload data
group.upper_central_series
Upper central series of a group
mf.upper_half_plane
Upper half-plane
V
character.dirichlet.values
Values of a Dirichlet character
character.dirichlet.values_on_gens
Values of a Dirichlet character on generators
mf.siegel.family.sp4z_2
Vector valued Siegel modular forms of degree 2 taking values in three-dimensional space
mf.siegel.vector_valued
Vector-valued Siegel modular forms
mf.siegel.vector_valued_degree_two
Vector-valued Siegel modular forms of degree 2
lf.visible_slopes
Visible slopes
W
av.weak_equivalence_class
weak equivalence
av.fq.weak_equivalence_class
Weak equivalence class
ec.weierstrass_coeffs
Weierstrass equation or model
g2c.num_rat_wpts
Weierstrass points of a hyperelliptic curve
hgm.weight
weight
mf.siegel.weight_k_j
Weight
mf.bianchi.weight2
Weight 2 Bianchi modular forms
mf.slash_action
Weight $k$ slash-action
mf.bianchi.weight
Weight of a Bianchi modular form
mf.hilbert.weight_vector
Weight of a Hilbert modular form
st_group.weight
Weight of a Sato-Tate group
mf.siegel.weight
Weight of a Siegel modular form
cmf.weight
Weight of an elliptic modular form
nf.weil_height
Weil height
ec.q.weil_height
Weil height of a point on an elliptic curve over $\Q$
nf.weil_polynomial
Weil polynomial
group.weyl_group
Weyl group
group.fuchsian.cusps.width
Width of a cusp
mot.width
Width of a motive
doc.wiki
Wiki (definition)
lf.wild_inertia_group
Wild inertia group
lf.wild_inertia_group_search
Wild inertia group search
hgm.wild
Wild primes for hypergeometric families
lf.wild_slopes
Wild slopes of a local field
group.wreath_product
Wreath product
X
modcurve.xfull
$X(N)$
hmsurface.x0
$X_0(\mathfrak{N})_{\mathfrak{b}}$
modcurve.x0
$X_0(N)$
hmsurface.x01
$X_0^1(\mathfrak{N})_{\mathfrak{b}}$
modcurve.x1mn
$X_1(M,MN)$
modcurve.x1
$X_1(N)$
modcurve.xarith
$X_{\mathrm{arith}}(N)$
modcurve.xpm1
$X_{\pm 1}(N)$
modcurve.xpm1mn
$X_{\pm1}(M,MN)$
modcurve.xs4
$X_{S_4}(\ell)$
modcurve.xns
$X_{\text{ns}}(N)$
modcurve.xns_plus
$X_{\text{ns}}^+(N)$
modcurve.xsp
$X_{\text{sp}}(N)$
modcurve.xsp_plus
$X_{\text{sp}}^+(N)$
Z
lfunction.zfunction
Z-function of an L-function
group.z_group
Z-group
ring.zero_divisor
Zero divisor
lfunction.zeros
Zeros of an L-function
hgm.zigzagplot
Zigzag plot
2
g2c.two_selmer_rank
2-Selmer rank
g2c.two_torsion_field
2-torsion field
?
curve.highergenus.aut.sort_order
hgm.signature