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A
lfunction.history A history of L-functions
st_group.abelian Abelian
ag.abelian_surface Abelian surface
ag.abelian_variety Abelian variety
varieties.about About varieties
g2c.abs_discriminant Absolute discriminant
group.galois.absolute Absolute Galois group
ec.additive_reduction Additive reduction
nf.algebraic_closure Algebraic closure of a field
ag.curve Algebraic curve
mf.gl2.history.varieties Algebraic varieties
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.analytic_rank Analytic rank
g2c.analytic_rank Analytic rank bound
lfunction.arithmetic Arithmetic L-function
nf.arithmetically_equivalent Arithmetically equivalent fields
artin.lfunction Artin L-function
lfunction.history.artin Artin L-functions
nf.assuming_grh Assuming GRH
mf.elliptic.atkinlehner Atkin-Lehner eigenvalue
mf.maass.mwf.atkinlehner Atkin-Lehner eigenvalues
mf.elliptic.atkin-lehner Atkin-Lehner operator $W_Q$ on $X_0(N)$
bio.selberg Atle Selberg
B
ec.base_change Base change
af.bernoulli_numbers Bernoulli numbers
mf.bianchi.bianchigroup Bianchi Groups
mf.bianchi.bianchimodularforms Bianchi modular forms
ec.q.galois_rep_image_borel Borel case
C
g2c.277.a.277.1.top C277
ec.q.canonical_height Canonical height
lattice.catalogue_of_lattices Catalogue of Lattices
lfunction.central_character Central character of an L-function
lfunction.central_point Central point 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
gg.character_table.data Character table data
ag.cm_field CM field
mf.elliptic.cm_form CM form
mf.elliptic.coefficient_field Coefficient field for newforms
mf.gl2.history.combinatorics Combinatorcs and $q$-series
ec.complex_multiplication Complex multiplication
ag.complex_multiplication Complex multiplication
st_group.component_group Component group of a Sato-Tate group
st_group.components Components of a Sato-Tate group
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
data.congruent_numbers Congruent numbers data
gg.conjugacy_classes.data Conjugacy class representatives
gg.conjugacy_classes Conjugacy classes
st_group.connected Connected Sato-Tate group
character.dirichlet.conrey Conrey label of Dirichlet characters
artin.permutation_container Containing permutation representation
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
mf.elliptic.cusp_form Cusp form (elliptic)
D
lf.field.data Data for a local field
mf.half_integral_weight.dedekind_eta Dedekind eta function
lfunction.history.dedekind Dedekind zeta-functions, history
lf.defining_polynomial Defining polynomial of a local field
nf.defining_polynomial Defining Polynomial of a Number Field
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
st_group.degree Degree of a Sato-Tate group
lfunction.degree 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
character.dirichlet Dirichlet character
dq.character.dirichlet.extent Dirichlet character data extent
character.dirichlet.group 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
mf.1.12.1.a.top Discriminant modular form
lf.discriminant_root_field Discriminant root field of a local field
ec.discriminant_valuation Discriminant valuation
af.divisor_function Divisor function
bio.zagier Don Bernard Zagier
lattice.dual Dual lattice
mf.siegel.lift.ikeda Duke-Imamoglu-Ikeda lift
E
lattice.8.1.1.1.1.top E_8 Lattice
ec.q.37.a1.bottom Elliptic Curve 37a1
ec.q.66.c4.bottom Elliptic curve 66.c4
ec.q.858.k1.bottom Elliptic curve 858.k1
ec.q.invariants Elliptic curve invariants
mf.gl2.history.elliptic Elliptic functions
bio.artin Emil Artin
ag.endomorphism_algebra Endomorphism algebra
g2c.jac_endomorphisms Endomorphism invariants
g2c.jac_end_lattice Endomorphism lattice
ag.endomorphism_ring Endomorphism ring
mf.11.2.1.a.formulas Eta product for mf.11.2.1.a
mf.12.3.5.a.formulas Eta product for mf.12.3.5.a
mf.14.2.1.a.formulas Eta product for mf.14.2.1.a
mf.15.2.1.a.formulas Eta product for mf.15.2.1.a
mf.16.3.15.a.formulas Eta product for mf.16.3.15.a
mf.2.8.1.a.formulas Eta product for mf.2.8.1.a
mf.20.2.1.a.formulas Eta product for mf.20.2.1.a
mf.24.2.1.a.formulas Eta product for mf.24.2.1.a
mf.27.2.1.a.formulas Eta product for mf.27.2.1.a
mf.3.6.1.a.formulas Eta product for mf.3.6.1.a
mf.32.2.1.a.formulas Eta product for mf.32.2.1.a
mf.36.2.1.a.formulas Eta product for mf.36.2.1.a
mf.4.5.3.a.formulas Eta product for mf.4.5.3.a
mf.4.6.1.a.formulas Eta product for mf.4.6.1.a
mf.5.4.1.a.formulas Eta product for mf.5.4.1.a
mf.6.4.1.a.formulas Eta product for mf.6.4.1.a
mf.7.3.6.a.formulas Eta product for mf.7.3.6.a
mf.8.3.3.a.formulas Eta product for mf.8.3.3.a
mf.8.4.1.a.formulas Eta product for mf.8.4.1.a
mf.9.4.1.a.formulas Eta product for mf.9.4.1.a
mf.144.2.1.a.formulas Eta quotient for mf.144.2.1.a
mf.48.2.1.a.formulas Eta quotient for mf.48.2.1.a
mf.64.2.1.a.formulas Eta quotient for mf.64.2.1.a
mf.80.2.1.b.formulas Eta quotient for mf.80.2.1.b
mf.half_integral_weight.eta_quotients Eta quotients
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
ec.q.galois_rep_image_exc Exceptional case
doc.view_knowl Expand a knowl
dq.zeros.zeta.extent Extent of Riemann zeta zeros data
F
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
field.about Fields
mf.1.12.1.a.formulas Formula for mf.1.12.1a
mf.elliptic.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.maass.mwf.fricke Fricke eigenvalue
mf.elliptic.fricke Fricke involution for Gamma_0
nf.frobenius_cycle_types Frobenius cycle types
artin.frobenius_schur_indicator Frobenius-Schur indicator of a representation
group.fuchsian Fuchsian group
lfunction.functional_equation Functional equation of an L-function
group.fuchsian.fundamental_domain Fundamental domain
group.sl2z.fundamental_domain Fundamental domain of SL$_2\mathbb{Z}$
G
nf.galois_closure Galois closure of an extension
gg.galois_group Galois group
nf.galois_group.data 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
st_group.generators Generators of a Sato-Tate group
character.dirichlet.values_on_gens Generators of the group of Dirichlet characters
g2c.g2curve Genus 2 curve
g2c.249.a.249.1.top Genus 2 curve 249.a.249.1
g2c.997.b.997.1.top Genus 2 curve 997.b.997.1
g2c.1116.a.214272.1.top Genus 2 curve of conductor 1116
g2c.976.a.999424.1.top Genus 2 curve of conductor 976
ag.curve.genus Genus of a smooth curve
group.sl2z.genus_subgroup Genus of a subgroup of the modular group
g2c.geom_aut_grp Geometric automorphism group
ag.geom_simple Geometrically simple
ec.global_minimal_model Global minimal model
ec.good_reduction Good reduction
lattice.gram Gram matrix
mf.siegel.lift.gritsenko Gritsenko lift
group.gammann Group $\Gamma(N)$
gg.group_action_invariants Group action Invariants
gg.invariants Group invariants
group.about Groups
H
mf.half_integral_weight Half-integral weight modular forms
bio.harald_schilly Harald Schilly
nf.17.1.604462909807314587353088.1.bottom Harbater number field
g2c.has_square_sha Has square Ш
lfunction.history.hasse_weil Hasse-Weil L-function
character.hecke Hecke character
mf.gl2.history.hecke Hecke Characters
lfunction.history.hecke_characters Hecke L-functions
mf.elliptic.hecke-operator Hecke operator of index $n$
lfunction.history.hecke_operators Hecke operators, history
mf.elliptic.hecke-orbit Hecke orbit
lattice.hermite_number Hermite number
hgm.field.label HGM Labels
crystals.highest_weight Highest weight crystals
lattice.history History of Lattices
mf.elliptic.eisenstein Holomorphic Eisenstein series
abvar.fq.honda_tate Honda-Tate Theorem
content.how-to-cite How to cite the LMFDB
mf.upper-half-plane Hyperbolic 2-space
mf.bianchi.hyperbolic3space Hyperbolic 3-space
I
ec.conductor_norm Ideal norm of conductor
doc.knowl.identifier Identifier of a knowl
st_group.identity_component Identity component of a Sato-Tate group
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
group.subgroup.index Index of a normal subgroup
intro.description Index page, first sentences
mf.gl2.history.infinite Infinite products
nf.integral Integral elements
lattice.definition Integral Lattice
ec.integral_model Integral model
ec.q.integral_points Integral points
nf.intermediate_fields Intermediate fields
intro Introduction
intro.features Introduction/Features
lfunction.invariants Invariants of an L-function
abvar.decomposition.data Isogeny factor decomposition data
ec.weierstrass_isomorphism Isomorphism between Weierstrass models
J
ec.j_invariant_denominator_valuation j-invariant denominator valuation
mf.jacobi Jacobi forms
character.dirichlet.jacobi_sum Jacobi sum
ag.jacobian Jacobian of a curve
bio.serre Jean-Pierre Serre
K
lattice.kissing Kissing Number
character.dirichlet.kloosterman_sum Kloosterman sum
doc.knowl Knowl
doc.knowl.guidelines Knowl Edit Guidelines
test.knowlparam Knowl with parameters
ec.q.kodaira_symbol Kodaira symbol
ec.kodaira_symbol Kodaira symbol
character.dirichlet.kronecker_symbol Kronecker symbol
L
lfunction.definition L-function
lfunction.spectral_parameters L-function spectral parameters
lfunction.history.maass L-functions of Maass forms
mf.elliptic.character.label Label convention for Dirichlet characters
lf.field.label Label for a local field
lfunction.history.langlands_program Langlands program
lfunction.degree4.1.34260324.bottom Large gap between nontrivial zeros
character.dirichlet.conrey.primitive_generator least primitive root modulo p^e
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
mf.siegel.lift Lift Siegel modular form
crystals.littelmann_path Littelmann path model for crystals
doc.lmfdb.improve LMFDB backend
doc.news.in_the_news LMFDB in the news
lf.invariants Local field invariants
ec.local_minimal_discriminant Local minimal discriminant of an elliptic curve
ec.local_minimal_model Local minimal model
ec.local_root_number Local root number
g2c.locally_solvable Locally solvable
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
M
mf.maass.mwf.browsegraph Maass form browsing graph explanation
mf.maass.mwf Maass form on GL2(R)
mf.maass.mwf.weight0 Maass forms of weight 0
mf.maass.picard Maass forms on PSL(2,Z[i])
content.edit-board Management board
uploader.mapping_rules Mapping rules
st_group.subgroups Maximal subgroups
ec.q.3675.g1.top Minimal 17-congruence
ec.q.47775.be1 Minimal 17-congruence
ec.minimal_discriminant Minimal discriminant
ec.minimal_discriminant_norm Minimal discriminant norm
mf.elliptic.minimal Minimal modular form
nf.minimal_polynomial Minimal polynomial
st_group.supgroups Minimal supergroups
ec.q.minimal_weierstrass_equation Minimal Weierstrass equation over $\mathbb Q$
lattice.minimal_vector Minimum vector length
mf.siegel.lift.miyawaki Miyawaki lift
mf.siegel.lift.miyawaki2 Miyawaki lift of type II
ec.q.11.a2.top Modular curve $X_0(11)$
ec.q.14.a6.top Modular curve $X_0(14)$
ec.q.15.a5.top Modular curve $X_0(15)$
ec.q.17.a3.top Modular curve $X_0(17)$
ec.q.19.a2.top Modular curve $X_0(19)$
ec.q.20.a4.top Modular curve $X_0(20)$
ec.q.21.a5.top Modular curve $X_0(21)$
ec.q.24.a4.top Modular curve $X_0(24)$
g2c.676.a.562432.1.top Modular curve $X_0(26)$
ec.q.27.a3.top Modular curve $X_0(27)$
g2c.196.a.21952.1.top Modular curve $X_0(28)$
g2c.450.a.36450.1.top Modular curve $X_0(3)/W_{10}$
g2c.961.a.923521.1.top Modular curve $X_0(31)$
ec.q.32.a4.top Modular curve $X_0(32)$
ec.q.36.a4.top Modular curve $X_0(36)$
g2c.1369.a.50653.1.top Modular curve $X_0(37)$
ec.q.49.a4.top Modular curve $X_0(49)$
g2c.2500.a.50000.1.top Modular curve $X_0(50)$
ag.modcurve.x0 Modular curve $X_0(N)$
ec.q.11.a3.top Modular curve $X_1(11)$
g2c.169.a.169.1.top Modular curve $X_1(13)$
ec.q.14.a5.top Modular curve $X_1(14)$
ec.q.15.a7.top Modular curve $X_1(15)$
g2c.256.a.512.1.top Modular curve $X_1(16)$
g2c.324.a.648.1.top Modular curve $X_1(18)$
ag.modcurve.x1 Modular curve $X_1(N)$
character.dirichlet.modulus Modulus of a Dirichlet character
st_group.moments Moment statistics
ec.mordell_weil Mordell-Weil group
ec.mordell-weil Mordell-Weil theorem
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
N
lattice.name 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
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
lfunction.normalization Normalization of an L-function
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
O
character.dirichlet.order Order of a Dirichlet character
character.dirichlet.conrey.order Order of a Dirichlet character from its label
group.order Order of a group
P
abvar.fq.p_rank p-rank
group.paramodular Paramodular group
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
mf.elliptic.petersson-scalar-product Petersson scalar product
mf.gl2.history.poincare Poincaré series
specialfunction.poincare Poincaré series
doc.lmfdb.contextualize Presentation of the data in the LMFDB
ag.bad_prime Prime of bad reduction
g2c.good_reduction Primes of good reduction
character.dirichlet.primitive Primitive Dirichlet character
lattice.primitive Primitive integral lattice
lfunction.primitive Primitive L-function
gg.4t3.bottom Properties of D_4
character.dirichlet.basic_properties Properties of Dirichlet characters
Q
mf.hilbert.q_expansion q-expansion of a Hilbert modular form
mf.elliptic.q-expansion q-expansion of an elliptic modular form
mf.quasi_modular Quasi-modular form
R
lfunction.history.ramanujan_tau Ramanujan tau L-function
lfunction.history.rankin_selberg Ranking-Selberg convolution, history
st_group.real_dimension Real dimension of a Sato-Tate group
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
mf.gl2.history.remainder Remainder terms
repn.about Representation
bio.borcherds Richard Ewen Borcherds
lfunction.riemann Riemann zeta-function
lfunction.history.riemanns_memoir Riemann's memoir
character.dirichlet.roadmap Roadmap for Dirichlet characters
lfunction.roadmap Roadmap for L-functions
mf.maass.roadmap Roadmap for Maass forms
ec.q.rouse-classification Rouse classification
ec.rouse_label Rouse label
S
sage.cellexample Sage cell example
sage.test Sage cell knowl
mf.siegel.lift.saito_kurokawa Saito-Kurokawa lift
st_group.definition Sato-Tate group
ag.sato_tate_group Sato-Tate group (of a motive)
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.roadmap Sato-Tate group roadmap
st_group.subsupgroups Sato-Tate subgroups and supergroups
ec.q.21168.ce2.top 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
ec.semi_global_minimal_model Semi-global minimal model
nf.separable Separable extension
mf.elliptic.shimura_correspondence Shimura correspondence
mf.half_integral_weight.shimura_decomposition Shimura decomposition
nf.sibling Sibling fields
gg.other_representations Siblings for a Galois group
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
lfunction.history.siegel Siegel modular forms, history
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
gg.solvable Solvable group
dq.character.dirichlet.source Source of Dirichlet character computations
dq.lattice.source Source of lattice data
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
mf.sturm_bound Sturm bound
gg.subfields Subfields
gg.subnormal_series Subnormal series
ec.q.surjective_prime Surjective prime
group.sp2gr Symplectic group
T
zeros.first.contents Table of first zeros of L-function
ec.tamagawa_number Tamagawa number
ec.padic_tate_module Tate module of an elliptic curve
lfunction.history.tates_thesis Tate's thesis
lfunction.taxonomy Taxonomy of L-functions
test.text Test → !!!
mf.maass.mwf.eigenvalue The eigenvalue of a Maass form
lattice.24.1.1.0.1.top The Leech lattice
lattice.24.1.1.24.1.top The Leech lattice
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
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
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
nf.sextic_twin Twin sextic algebra
U
lfunction.underlying_object Underlying object of an L-function
doc.upload_data Upload data
mf.upper_half_plane Upper half-pane
V
lfunction.value Value of an L-function
character.dirichlet.values Values of a Dirichlet character
mf.siegel.vector_valued Vector-valued Siegel modular forms
W
ec.weierstrass_coeffs Weierstrass equation or model
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
abvar.fq.weil-polynomial Weil q-Polynomials
group.fuchsian.cusps.width Width of a cusp
mot.width Width of a motive
bio.william_stein William Stein
Z
lfunction.zfunction Z-function of an L-function
lfunction.zeros Zeros of an L-function
?
lfunction.riemann.bottom
mf.maass.mwf.plot
sage.cell
users.pascal.note
content.news
doc.related_to "related to" field
g2c.gl2type $\GL_2$-type
ec.q_curve $\mathbb{Q}$-curves
specialfunction.k_bessel $K$-Bessel functions
nf.20.2.558854584859141340505879659895771.1.bottom 19-division field for CM elliptic curve for $\Q(\sqrt{-7})$
g2c.two_selmer_rank 2-Selmer rank
ec.q.2450.a1.top 2450.a1