Filter Category: af(4) ag(59) alg(7) artin(23) av(48) belyi(19) character(43) clusterpicture(1) cmf(89) combin(1) commensurable(1) content(3) crystals(3) curve(18) doc(23) dq(33) ec(118) field(1) g2c(57) gg(24) gl2(15) group(167) gsp4(1) hecke_algebra(1) hgm(18) hmsurface(18) intro(5) lattice(27) lf(47) lfunction(71) lmfdb(1) lucant(1) mf(135) modcurve(58) modlgal(25) modlgalrep(2) mot(2) motives(1) nf(96) paramodulargroup(1) portrait(4) rcs(138) repn(3) ring(22) sage(3) sh(2) shimcurve(14) specialfunction(3) st_group(34) stats(3) test(3) users(2) varieties(1) zeros(1)
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More Recently modified knowls
curve.highergenus.aut.group_action A group acting on a compact Riemann Surface
lfunction.history A history of L-functions
ring.a-field $A$-field
group.a_group A-group
group.abelian Abelian group
ag.abelian_surface Abelian surface
ag.abelian_variety Abelian variety
group.abelianization Abelianization
group.abelianization_isolabel Abelianization label
varieties.about About varieties
g2c.abs_discriminant Absolute discriminant
modlgal.absolute_frobenius Absolute Frobenius
group.galois.absolute Absolute Galois group
nf.absolute_value Absolute value of a field
modlgal.absolutely_irreducible Absolutely irreducible Abstract group name
rcs.ack.groups.abstract Acknowledgements for abstract groups
rcs.ack.character.dirichlet Acknowledgments for Dirichlet characters Acknowledgments for hosting
rcs.ack.meetings Acknowledgments for meetings Acknowledgments for software
rcs.ack.sponsors Acknowledgments for sponsors
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
nf.class_number_formula Analytic class number formula
lfunction.analytic_conductor Analytic conductor
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
g2c.analytic_rank Analytic rank of a curve
av.fq.angle_rank Angle rank of a set
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.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
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
lattice.automorphism_group Automorphism group of an integral lattice
group.automorphism Automorphisms of a group Available samples for $M_2(K(p))$
cmf.bad_prime Bad prime
lfunction.bad_prime Bad prime
ag.base_change Base change
ec.base_change Base change
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
af.bernoulli_numbers Bernoulli numbers
mf.bianchi.bianchigroup Bianchi Groups
mf.bianchi.bianchimodularforms Bianchi modular forms
mf.bianchi.newform Bianchi newform
alg.binary_operation Binary operation
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
ec.q.canonical_height Canonical height
ag.canonical_model Canonical model
gl2.cartan Cartan subgroup
lattice.catalogue_of_lattices Catalogue of Lattices
group.center_isolabel Center label Center of a character 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 Character table data
ring.characteristic Characteristic of a ring
modlgal.frobenius_charpoly Characteristic polynomial of Frobenius
group.characteristic_subgroup Characteristic subgroup
group.chief_series Chief series of a group
ag.cluster_picture Cluster picture 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
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.character.dirichlet Completeness of Dirichlet character data
rcs.cande.lfunction Completeness of L-function Data
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
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
g2c.conditional_mw_group Conditional Mordell-Weil group
av.endomorphism_ring_conductor Conductor
modlgal.conductor Conductor
character.dirichlet.conductor Conductor of a Dirichlet character
character.dirichlet.conrey.conductor Conductor of a Dirichlet character from its Conrey label
lfunction.conductor Conductor of an L-function
ec.conductor_valuation Conductor valuation
cmf.congruence_subgroup Congruence subgroup
hmsurface.congruence_subgroup Congruence Subgroup
mf.bianchi.bianchicongruencesubgroup Congruence subgroup of a Bianchi group
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 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.cyclic Cyclic group
ag.cyclic_trigonal Cyclic trigonal curve
D Data for a cluster picture Data for a dirichlet character
character.dirichlet.orbit_data Data for a Galois orbit of Dirichlet characters Data for a local field Data on small group Decomposition into newforms
cmf.dim_decomposition Decomposition into newforms Decomposition into newforms for Gamma1(N)
ring.dedekind_domain Dedekind domain
mf.half_integral_weight.dedekind_eta Dedekind eta function
lfunction.history.dedekind Dedekind zeta-functions, history
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
hmsurface.level Definition of the level 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 Degree of a Belyi map
group.representation.complex_char_deg Degree of a character Degree of a Dirichlet character
modcurve.point_degree Degree of a point on a modular curve Degree of a Sato-Tate group Degree of an L-function
av.deligne_module Deligne module
group.derived_series Derived series of a group
doc.knowl.description Description field in knowls
cmf.statistics_extent Description of completeness
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
cmf.atkin_lehner_dims Dimensions of Atkin-Lehner subspaces
group.direct_product Direct product of groups
character.dirichlet Dirichlet character
dq.character.dirichlet.extent Dirichlet character data extent Dirichlet character group
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
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
lf.eisenstein_polynomial Eisenstein polynomial
group.elementary Elementary group
modcurve.elliptic_curve_of_point Elliptic curve associated to a rational point
ec.q.invariants Elliptic curve invariants
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
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
ag.endomorphism_ring Endomorphism ring
av.fq.endomorphism_ring_notation Endomorphism ring notation
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
gl2.exceptional Exceptional subgroup
doc.view_knowl Expand a knowl
group.exponent Exponent of a group
dq.hecke_algebras.extent Extent of data for Hecke Algebras
group.order_factorization Factorization of the group order
group.representation.faithful Faithful representation
ec.q.faltings_ratio Faltings ratio Family of Siegel groups
modcurve.fiber_product Fiber product
ring.field Field
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
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
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.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 Galois group information
lf.galois_invariants Galois invariants of a local field
lf.galois_mean_slope Galois mean slope
nf.galois_group.gmodule Galois module information
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
cmf.galois_representation Galois representation
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
modlgal.generating_primes Generating Frobenius classes
curve.highergenus.aut.generatingvector Generating Vector
nf.field_generator Generator of a number field 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
group.sl2z.genus_subgroup Genus of a subgroup of the modular group
modcurve.genus_minus_rank Genus-rank difference
g2c.geom_aut_grp Geometric automorphism group
ag.geom_component Geometric component
ag.geom_endomorphism_algebra 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
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
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
group.homomorphism Group homomorphism
gg.invariants Group invariants
group.isomorphism Group isomorphism
group.about Groups
gsp4.subgroup_data GSp4 subgroup data
doc.knowl.annotation_guidelines Guidelines for writing annotations
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
hgm.field.label HGM Labels
crystals.highest_weight Highest weight crystals
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
ag.holomorphic_euler_char Holomorphic Euler characteristic
av.fq.honda_tate Honda-Tate theorem
rcs.cite.groups.abstract How to cite abstract groups
rcs.cite.belyi How to cite Belyi maps How to cite Bianchi modular forms
rcs.cite.character.dirichlet How to cite Dirichlet characters How to cite Hilbert modular forms
rcs.cite.lfunction How to cite L-functions
rcs.cite.maass How to cite Maass forms
rcs.cite.st_group How to cite Sato-Tate groups
content.how_to_cite How to cite the LMFDB
curve.highergenus.hurwitz_bound Hurwitz bound
mf.bianchi.hyperbolic3space Hyperbolic 3-space
group.hyperelementary Hyperelementary group
ag.hyperelliptic_curve Hyperelliptic curve
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_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
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
cmf.include_all_spaces Include all spaces
modcurve.index Index of a modular curve
modcurve.relative_index Index of a modular map
shimcurve.index Index of a Shimura curve
group.subgroup.index Index of a subgroup
av.fq.zfv_index Index of maximal order
av.fq.zfv_real_index Index of Real Order
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
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
ring.integral_domain Integral domain
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
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
ag.irreducible Irreducible variety
nf.is_galois Is a Galois extension
group.isoclinism Isoclinism Isogeny class data
ec.isogeny_class_degree Isogeny class degree
ec.isogenygraph.legend Isogeny graph legend
ag.isolated_point Isolated point
modcurve.isolated_point Isolated point on a modular curve
ec.weierstrass_isomorphism Isomorphism between Weierstrass models
ec.j_invariant_denominator_valuation j-invariant denominator valuation
modcurve.j_invariant_map $j$-invariant map
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
lf.jump_set Jump set
specialfunction.k_bessel $K$-Bessel functions
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
lfunction L-function
lfunction.spectral_parameters L-function spectral parameters
lfunction.history.maass L-functions of Maass forms
group.label_conjugacy_class Label of a conjugacy class
character.dirichlet.galois_orbit_label Label of a Galois orbit of a Dirichlet character
group.label Label of a group
modcurve.label Label of a modular curve
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
character.dirichlet.conrey.orbit_label Labels for Galois orbits of Dirichlet Characters
lfunction.history.langlands_program Langlands program
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.hilbert.level_norm Level of a Hilbert modular form
modcurve.level Level of a modular curve
shimcurve.level Level of a Shimura curve
modcurve.level_structure Level structure of a modular curve
mf.siegel.lift Lift Siegel modular form
crystals.littelmann_path Littelmann path model for crystals
doc.lmfdb.improve LMFDB backend LMFDB Press Local algebra
nf.local_algebra Local algebra
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
mf.maass.mwf.coefficients Maass form coefficients
mf.maass.mwf.plot Maass form plot
mf.maass.mwf.weight0 Maass forms of weight 0
mf.maass.picard Maass forms on PSL(2,Z[i])
content.edit_board Management board
ec.q_curve $\mathbb{Q}$-curves
group.matrix_group Matrix 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
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
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
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.miyawaki2 Miyawaki lift of type II
g2c.galois_rep_modell_image Mod-$\ell$ Galois image of a genus 2 curve
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 $X_1(N)$
mf.about Modular Forms
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
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
g2c.mordell_weil_rank Mordell-Weil rank
ec.mordell_weil_theorem Mordell-Weil theorem
motives.about Motives
lfunction.motivic_weight Motivic weight
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 Name of a lattice
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
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
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.invariants Number field invariants
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
cmf.decomposition.old.gamma1 Oldspace decomposition for Gamma1(N)
cmf.decomposition.old.gamma0chi Oldspace decomposition for newform space Open subgroup
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 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_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
lf.padic_field $p$-adic field
group.pgroup $p$-group
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
belyi.passport Passport
belyi.passport_label Passport label
group.perfect Perfect groups
group.permutation_degree Permutation degree
group.permutation_representation Permutation representation
cmf.petersson_scalar_product Petersson scalar product
cmf.picture_description Pictures for classical modular forms
portrait.modcurve Pictures of modular curves
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
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
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
ag.bad_prime Prime of bad reduction
g2c.good_reduction Primes of good reduction
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
belyi.primitivization Primitivization of a Belyi map
character.dirichlet.principal Principal Dirichlet character
ring.principal_fractional_ideal Principal fractional ideal
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_type Projective image type
ag.projective_space Projective space
group.proper_subgroup Proper subgroup
stats.proportions Proportions for statistics
modcurve.psl2index $\PSL_2$-index
mf.hilbert.q_expansion q-expansion of a Hilbert 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
group.radical Radical of a group
lfunction.history.ramanujan_tau Ramanujan tau L-function
lf.ramification_polygon Ramification polygon
lf.ramification_polygon_display Ramification polygon
belyi.ramification_type Ramification type
group.rank Rank
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_type Reduction type
curve.highergenus.aut.refinedpassport Refined passport
nf.reflex_field Reflex field
nf.reflex_reflex_field Reflex field of the reflex field
doc.related_to Related objects
cmf.relative_dimension Relative dimension
av.fq.zfv_rel_disc_norm Relative discriminant norm
rcs.rigor.groups.abstract Reliability of abstract groups data 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 Reliability of L-function data
rcs.rigor.lattice Reliability of lattice data
rcs.rigor.lfunction.maass Reliability of Maass form L-function data
rcs.rigor.lfunction.modular Reliability of Modular L-function Data
mf.gl2.history.remainder Remainder terms
doc.knowl.rename Renaming a knowl
repn.about Representation
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
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
character.dirichlet.roadmap Roadmap for Dirichlet characters
lfunction.roadmap Roadmap for L-functions
mf.maass.roadmap Roadmap for Maass 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
lattice.root_lattice Root lattice
ec.rouse_label Rouse label
sage.test Sage cell knowl
sage.cell Sage cell server
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) 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
st_group.subsupgroups Sato-Tate subgroups and supergroups
group.representation.schur_index Schur index
group.schur_multiplier Schur multiplier Search
doc.search_columns Search columns
ec.galois_image_search Searching on Galois images
st_group.second_trace_moment Second trace moment
lfunction.selberg_class.axioms Selberg class axioms
lfunction.selberg_class Selberg class of L-functions
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
cmf.self_twist Self-twist
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
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
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
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.halfspace Siegel upper half-space
mf.bianchi.sign Sign of a Bianchi newform
lfunction.root_number Sign of an L-function
curve.highergenus.aut.signature Signature of a group action on a curve
lfunction.signature Signature of an L-function
ag.simple Simple
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.quotient_size Size of a quotient
modcurve.sl2level $\SL_2$-level
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
dq.belyi.source Source of Belyi maps data
rcs.source.belyi Source of Belyi maps data Source of Bianchi modular form data
rcs.source.character.dirichlet Source of Dirichlet character data
rcs.source.lfunction.dirichlet Source of Dirichlet L-function Data Source of Hilbert modular form data
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.modcurve Source of modular curve data
rcs.source.lfunction.modular Source of Modular L-function Data
rcs.source.zeros.zeta Source of Riemann Zeta Zeros Data
rcs.source.st_group Source of Sato-Tate Group Data Source of Siegel modular form data
cmf.newspaces Space of newforms
mf.siegel.newspace Space of paramodular newforms
lfunction.spectral_label Spectral label
gl2.split_cartan Split Cartan subgroup
ec.split_multiplicative_reduction Split multiplicative reduction
ag.splitting_field Splitting field
curve.highergenus.aut.generators Standard generators
hmsurface.standard_hmsurfaces Standard Hilbert modular surfaces Standard modular curves
modcurve.standard Standard modular curves
group.stem_extension Stem extension
group.stem_group Stem group 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.subgroup_isolabel Subgroup label
group.subgroup_label Subgroup labels
group.subgroup Subgroup of a group
gg.subnormal_series Subnormal series Subspaces of degree 2 Siegel modular forms
av.fq.supersingular Supersingular abelian variety
group.supersolvable Supersolvable group
modlgal.surjective Surjective
group.sylow_subgroup Sylow subgroup
group.symmetric Symmetric group
st_group.symplectic_form Symplectic form
group.sp2gr Symplectic group
alg.symplectic_isomorphism Symplectic isomorphism
zeros.first.contents Table of first zeros of L-function
ec.tamagawa_number Tamagawa number
g2c.tamagawa Tamagawa numbers
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
mf.maass.mwf.ncoefficients The number of coefficients
mf.maass.mwf.precision The precision of an eigenvalue
mf.maass.mwf.spectralparameter The spectral parameter of a Maass waveform
mf.maass.mwf.symmetry The symmetry of a Maass form
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
mf.half_integral_weight.theta Theta function
mf.gl2.history.theta Theta functions
dq.zeros.zeta.toomany Too many zeros
modlgal.top_slope Top slope
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
g2c.torsion Torsion subgroup
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
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
group.representation.type Type of a complex group representation
group.type Type of groups
group.under_subgroup Under-subgroup
lfunction.underlying_object Underlying object of an L-function
lattice.unimodular Unimodular lattice
ring.unique_factorization_domain Unique factorization domain
nf.torsion Unit group torsion
ring.unit Unit in a ring
lf.unramified_degree Unramified degree of a local field
modlgal.good_prime Unramified prime
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
character.dirichlet.values Values of a Dirichlet character
character.dirichlet.values_on_gens Values of a Dirichlet character on generators
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
av.weak_equivalence_class weak equivalence
av.fq.weak_equivalence_class Weak equivalence class
ec.weierstrass_coeffs Weierstrass equation or model
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.hilbert.weight_vector Weight of a Hilbert modular form
st_group.weight Weight of a Sato-Tate group
nf.weil_height Weil height
nf.weil_polynomial Weil polynomial
group.weyl_group Weyl group
group.fuchsian.cusps.width Width of a cusp
mot.width Width of a motive
lf.wild_inertia_group Wild inertia group
lf.wild_inertia_group_search Wild inertia group search
group.wreath_product Wreath product
modcurve.xfull $X(N)$
modcurve.x0 $X_0(N)$
modcurve.x1mn $X_1(M,MN)$
modcurve.x1 $X_1(N)$
modcurve.xsym $X_{\mathrm{sym}}(N)$
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 $X_{\text{sp}}^+(N)$
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
g2c.two_selmer_rank 2-Selmer rank
g2c.two_torsion_field 2-torsion field