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ag.abelian_surface Abelian surface
ag.abelian_variety Abelian variety
g2c.abs_discriminant Absolute discriminant
group.galois.absolute Absolute Galois group
ec.additive_reduction Additive reduction
ag.curve Algebraic curve
ag.variety Algebraic variety
ec.q.analytic_sha_order Analytic order of Ш
ec.q.analytic_sha_value Analytic order of Sha (numerical value)
lfunction.arithmetic Arithmetic L-function
artin.lfunction Artin L-function
nf.assuming_grh Assuming GRH
mf.elliptic.atkinlehner Atkin-Lehner eigenvalue
mf.maass.mwf.atkinlehner Atkin-Lehner eigenvalues
bio.selberg Atle Selberg
ec.base_change Base change
mf.bianchi.bianchigroup Bianchi Groups
mf.bianchi.bianchimodularforms Bianchi modular forms
ec.q.galois_rep_image_borel Borel case
ec.q.canonical_height Canonical height
lfunction.central_character Central character of an L-function
lfunction.central_value Central value of an L-function
mf.maass.mwf.character Character of a Maass form
mf.elliptic.character Character of a modular form Character table data
ag.cm_field CM field
ec.complex_multiplication Complex multiplication
ag.complex_multiplication Complex multiplication
character.dirichlet.conductor Conductor of a Dirichlet character
lfunction.conductor Conductor of an L-function
ec.conductor_valuation Conductor valuation
data.congruent_numbers Congruent numbers data Conjugacy class representatives
gg.conjugacy_classes Conjugacy classes
riemann.stieltjes.contents Contents of our Stieltjes constants tables
doc.create_knowl Create a knowl
doc.create_account Create an account
ec.q.cremona_label Cremona label
lfunction.critical_line Critical line of an L-function
lfunction.critical_strip Critical strip
crystals.crystal Crystal
mf.elliptic.cusp_form Cusp form (elliptic)
lf.defining_polynomial Defining polynomial of a local field
nf.defining_polynomial Defining Polynomial of a Number Field 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 an L-function
doc.knowl.description Description field in knowls
doc.development Developers Guide
mf.hilbert.dimension Dimension of a Hecke constituent
mf.elliptic.dimension_galois_orbit Dimension of a Hecke orbit
mf.elliptic.hecke-orbit-dimension Dimension of a Hecke orbit
character.dirichlet Dirichlet character Dirichlet character group
lfunction.dirichlet Dirichlet L-function
lfunction.dirichlet_series Dirichlet series
lf.discriminant_exponent Discriminant exponent of a local field
lf.discriminant_root_field Discriminant root field of a local field
ec.discriminant_valuation Discriminant valuation
mf.siegel.lift.ikeda Duke-Imamoglu-Ikeda lift
local_data ec.local_data
content.edit-board Editorial board and management
ec.q.37.a1.bottom Elliptic Curve 37a1
ec.q.invariants Elliptic curve invariants
bio.artin Emil Artin
ag.endomorphism_algebra Endomorphism algebra
g2c.jac_endomorphisms Endomorphism invariants
ec.q.endomorphism_ring Endomorphism ring
ec.endomorphism_ring Endomorphism ring
ag.endomorphism_ring Endomorphism ring
mf.11.2.0.a.formulas eta-product
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
ec.q.galois_rep_image_exc Exceptional case
doc.view_knowl Expand a knowl
nf.20.2.206007596521214410095208558252435839890349094339.1.bottom Field associated with 19-torsion on an elliptic curve
character.dirichlet.field_cut_out Field cut out by a Dirichlet character
character.dirichlet.field_values Field of values
mf.1.12.0.a.formulas Formulas for Delta(z)
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.maass.mwf.fricke Fricke eigenvalue
nf.frobenius_cycle_types Frobenius cycle types
artin.frobenius_schur_indicator Frobenius-Schur indicator of a representation
lfunction.functional_equation Functional equation of an L-function
gg.galois_group Galois group Galois group information
lf.galois_invariants Galois invariants of a local field
nf.galois_group.gmodule Galois module information
mf.elliptic.galois-orbits Galois orbit
mf.siegel.galois_orbit Galois orbit
character.dirichlet.galois_orbit Galois orbit of a Dirichlet character
character.dirichlet.gauss_sum Gauss sum
nf.field_generator Generator of a number field
character.dirichlet.values_on_gens Generators of the group of Dirichlet characters
g2c.g2curve Genus 2 curve
ag.curve.genus Genus of a smooth curve
g2c.geom_aut_grp Geometric automorphism group
ag.geom_simple Geometrically simple
ec.global_minimal_model Global minimal model
ec.good_reduction Good reduction
mf.siegel.lift.gritsenko Gritsenko lift
gg.group_action_invariants Group action Invariants
gg.invariants Group invariants
mf.half_integral_weight Half-integral weight modular forms
bio.harald_schilly Harald Schilly
nf.17.1.604462909807314587353088.1.bottom Harbater number field
mf.elliptic.hecke-orbit Hecke orbit
hgm.field.label HGM Labels
crystals.highest_weight Highest weight crystals How to cite the LMFDB
mf.upper-half-plane Hyperbolic 2-space
mf.bianchi.hyperbolic3space Hyperbolic 3-space
ec.conductor_norm Ideal norm of conductor
doc.knowl.identifier Identifier of a knowl
g2c.igusa_clebsch_invariants Igusa-Clebsch invariants of a genus 2 curve
ec.q.galois_rep_image Image of mod p Galois Representation
artin.gg_quotient Image of the representation
doc.knowl.implicit Implicit creation of knowls
intro.description Index page, first sentences
nf.integral Integral elements
ec.integral_model Integral model
ec.q.integral_points Integral points
nf.intermediate_fields Intermediate fields
intro Introduction
intro.features Introduction/Features
intro.tutorial Introduction/Tutorial
ec.j_invariant_denominator_valuation j-invariant denominator valuation
af.jacobi Jacobi forms
character.dirichlet.jacobi_sum Jacobi sum
ag.jacobian Jacobian of a curve
lattice.kissing Kissing Number
character.dirichlet.kloosterman_sum Kloosterman sum
doc.knowl Knowl
test.knowlparam Knowl with parameters
ec.q.kodaira_symbol Kodaira symbol
ec.kodaira_symbol Kodaira symbol
character.dirichlet.kronecker_symbol Kronecker symbol
lfunction.definition L-function
lfunction.spectral_parameters L-function spectral parameters
mf.elliptic.character.label Label convention for Dirichlet characters
lf.field.label Label for a local field
lfunction.degree2holo.key Legend for GL(2) holomorphic graph of dots
character.dirichlet.legendre_symbol Legendre symbol
bio.euler Leonhard Euler
mf.hilbert.level_norm Level of a Hilbert modular form
mf.elliptic.level Level of a modular form
lfunction.level Level of an L-function
crystals.littelmann_path Littelmann path model for crystals
doc.lmfdb.improve LMFDB backend
lf.invariants Local field invariants
ec.local_minimal_model Local minimal model
nf.14.2.79396891942519570432.1.bottom Low discriminant field
nf.14.2.536561726709678316933.1.bottom Low discriminant field
nf.17.1.239072435685151324847153.1.bottom Low discriminant field
nf.19.1.75613185918270483380568064.1.bottom Low discriminant field
mf.maass.mwf Maass form on GL2(R)
mf.maass.picard Maass forms on PSL(2,Z[i])
uploader.mapping_rules Mapping rules
ec.minimal_discriminant Minimal discriminant
ec.minimal_discriminant_norm Minimal discriminant norm
mf.elliptic.minimal Minimal modular form
ec.q.minimal_weierstrass_equation Minimal Weierstrass equation over $\mathbb Q$
demo.aim.mission_statement Mission statement of AIM
mf.siegel.lift.miyawaki Miyawaki lift Modular curve X_0(11) Modular curve X_1(11)
character.dirichlet.modulus Modulus of a Dirichlet character
ec.mordell_weil Mordell-Weil group
ec.mordell-weil Mordell-Weil theorem
nf.multiplicative_gal_module Multiplicative Galois Module Structure
ec.multiplicative_reduction Multiplicative reduction
mf.maass.mwf.dimension Multiplicity of an eigenvalue
doc.knowl.naming_conventions Naming conventions for knowls
doc.knowl.naming_suggestions Naming suggestions
mf.elliptic.newform Newform
ec.q.galois_rep_image_nsp_cartan Non-split Cartan case
ec.nonsplit_multiplicative_reduction Non-split multiplicative reduction
ec.q.non-surjective_prime Non-surjective prime
nf.14.2.20325604337285010030592.1.bottom Nonsolvable field ramified at 2 and 13
nf.18.2.40254497110927943179349807054456171205137.1.bottom Nonsolvable field ramified at only 17
ec.discriminant_norm Norm of discriminant
nf.defining_polynomial.normalization Normalization of defining polynomials for number fields
ec.q.galois_rep_image_norm_nsp_cartan Normalizer of the nonsplit Cartan case
ec.q.galois_rep_image_norm_sp_cartan Normalizer of the split Cartan case
nf.invariants Number field invariants
character.dirichlet.related_fields Number fields related to a Dirichlet character
demo.grassy_knoll obsolete
character.dirichlet.order Order of a Dirichlet character
group.order Order of a group
gg.other_representations Other representations of a group
P Paramodular group
mf.siegel.newform.paramodular Paramodular newform
character.dirichlet.parity Parity of a Dirichlet character
doc.lmfdb.contextualize Presentation of the data in the LMFDB
ag.bad_prime Prime of bad reduction
character.dirichlet.primitive Primitive Dirichlet character
lfunction.primitive Primitive L-function
character.dirichlet.basic_properties Properties of Dirichlet characters
mf.hilbert.q_expansion q-expansion of a Hilbert modular form
mf.elliptic.q-expansion q-expansion of an elliptic modular form
character.dirichlet.real Real Dirichlet character
ag.real_endomorphism_algebra Real endomorphism algebra
ag.real_multiplication Real multiplication
ec.q.real_period Real period
ec.reduction_type Reduction type
lfunction.riemann Riemann zeta-function
dirichlet_character.roadmap Roadmap for Dirichlet characters
character.dirichlet.roadmap Roadmap for Dirichlet characters
lfunction.roadmap Roadmap for L-functions
mf.maass.roadmap Roadmap for Maass forms
ec.rouse_label Rouse label
sage.cellexample Sage cell example
sage.test Sage cell knowl
mf.siegel.lift.saito_kurokawa Saito-Kurokawa lift
ag.sato_tate_group Sato-Tate group (of a motive)
g2c.st_group_identity_component Sato-Tate group identity component secp256k1 elliptic curve
lfunction.selberg_class.axioms Selberg class axioms
lfunction.selberg_class Selberg class of L-functions
lfunction.self-dual Self-dual L-function
nf.separable Separable extension
doc.lmfdb.share Sharing goal of the LMFDB
mf.elliptic.shimura_correspondence Shimura correspondence
mf.half_integral_weight.shimura_decomposition Shimura decomposition
mf.siegel.phi Siegel $\Phi$ operator
mf.siegel.cusp_form Siegel cusp form
mf.siegel.eisenstein_series Siegel Eisenstein series
mf.siegel.klingen_eisenstein_series Siegel Klingen-Eisenstein series
mf.siegel.hecke_operator Siegel modular form Hecke operators
mf.siegel.halfspace Siegel upper half space
lfunction.root_number Sign of an L-function
lfunction.signature Signature of an L-function
ag.simple Simple
gg.simple_name Simple group name
nf.14.2.35632953415471973197.1.bottom Small discriminant field
lfunction.special_values Special values of an L-function
ec.q.galois_rep_image_sp_cartan Split Cartan case
ec.split_multiplicative_reduction Split multiplicative reduction
riemann.stieltjes_constants Stieltjes constants
mf.sturm_bound Sturm bound
gg.subfields Subfields
ec.q.surjective_prime Surjective prime Symplectic group
zeros.first.contents Table of first zeros of L-function
ec.tamagawa_number Tamagawa number
lfunction.taxonomy Taxonomy of L-functions
test.text Test → !!!
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
nf.18.2.4768875488962616064464333777.1.bottom Torsion field
g2c.torsion_order Torsion order
ec.field.torsion_order Torsion order of an elliptic curve
g2c.torsion Torsion subgroup
nf.totally_imaginary Totally imaginary
nf.totally_positive Totally positive
nf.totally_real Totally real
artin.trace_of_complex_conj Trace of complex conjugation
doc.knowl.context_free Transclusion (definition)
mf.transformation_property Transformation property for modular forms
lfunction.underlying_object Underlying object of an L-function
doc.upload_data Upload data
lfunction.value Value of an L-function
character.dirichlet.values Values of a Dirichlet character
mf.siegel.vector_valued Vector-valued Siegel modular forms
ec.weierstrass_coeffs Weierstrass equation/coefficients
mf.hilbert.weight_vector Weight of a Hilbert modular form
nf_weil_height Weil height
mot.width Width of a motive
bio.william_stein William Stein
lfunction.zfunction Z-function of an L-function
lfunction.zeros Zeros of an L-function
doc.related_to "related to" field
g2c.gl2type $\GL_2$-type
nf.20.2.558854584859141340505879659895771.1.bottom 19-division field for CM elliptic curve for $\Q(\sqrt{-7})$
g2c.two_selmer_rank 2-Selmer rank 2450a1