- ID: drew

## Knowls

Andrew Sutherland has contributed to these Knowls:
$K$-gonality of a modular curve,
$X(N)$,
$X_0(N)$,
$X_1(M,MN)$,
$X_1(N)$,
$X_{S_4}(\ell)$,
$X_{\pm 1}(N)$,
$X_{\pm1}(M,MN)$,
$X_{\text{ns}}(N)$,
$X_{\text{ns}}^+(N)$,
$X_{\text{sp}}(N)$,
$X_{\text{sp}}^+(N)$,
$\GL_2$-type,
$\PSL_2$-index,
$\SL_2$-level,
$j$-invariant map,
$p$-adic field,
$p$-adic field (local number field),
2-Selmer rank,
2-torsion field,
A list of not so secret urls that aren't advertized,
A tour of the Riemann zeta function,
Abelian varieties with one rational point,
Abelian variety,
About varieties,
Absolute Frobenius,
Absolute discriminant,
Absolute value of a field,
Absolutely irreducible,
Acknowledgements for modular curve data,
Acknowledgments for (non-elliptic) curve L-functions,
Acknowledgments for Belyi maps,
Acknowledgments for Dirichlet characters,
Acknowledgments for Hilbert modular forms,
Acknowledgments for L-functions,
Acknowledgments for Maass form L-functions,
Acknowledgments for Maass forms,
Acknowledgments for Sato-Tate groups,
Acknowledgments for abelian varieties over finite fields,
Acknowledgments for classical modular forms,
Acknowledgments for curves of higher genus with automorphism group data,
Acknowledgments for elliptic curve L-functions,
Acknowledgments for genus 2 curves,
Acknowledgments for hosting,
Acknowledgments for hypergeometric motive data,
Acknowledgments for meetings,
Acknowledgments for modular form L-functions,
Acknowledgments for software,
Acknowledgments for sponsors,
Additional acknowledgments,
Algebraic variety ,
Ambient group of a Sato-Tate group,
Analytic class number formula,
Analytic conductor,
Analytic conductor of a classical newform,
Analytic order of Ш,
Analytic order of Sha,
Analytic order of Sha (numerical value),
Analytic rank,
Analytic rank,
Analytic rank,
Analytic rank of a curve,
Arithmetic L-function,
Arithmetic function,
Artin field,
Artin image,
Artin representation (definition),
Atkin-Lehner involution $w_Q$,
Automorphism group characters,
Automorphism group of an algebraic curve,
Available samples for $M_2(K(p))$,
Available samples for $M_k(\mathrm{Sp}(4,\mathbb{Z}))$,
Available samples for $M_k(\mathrm{Sp}(6,\mathbb{Z}))$,
Available samples for $M_k(\mathrm{Sp}(8,\mathbb{Z}))$,
Available samples for $M_{k,2}(\mathrm{Sp}(4,\mathbb{Z}))$,
BSD invariants,
Bad prime,
Base change,
Base field,
Base ring characteristic,
Basic properties of Dirichlet characters,
Bernoulli numbers,
Bianchi modular forms,
Birch and Swinnerton-Dyer conjecture,
Borel subgroup,
Branch Points,
Bézout matrix,
CM points,
Cartan subgroup,
Central value of an L-function,
Characteristic of a mod-$\ell$ Galois representation,
Characteristic of a ring,
Characteristic polynomial of Frobenius,
Classical modular form,
Codomain,
Codomain,
Coefficient field for newforms,
Coefficient field of an L-function,
Coefficient ring,
Coefficient ring generator bound,
Completeness and extent of Artin representation data,
Completeness and extent of Galois group data,
Completeness and extent of Maass form data,
Completeness and extent of global number field data,
Completeness of Bianchi Modular Form data,
Completeness of Bianchi modular form data,
Completeness of Classical Modular Form Data,
Completeness of Dirichlet character data,
Completeness of Hilbert modular form data,
Completeness of L-function Data,
Completeness of Riemann Zeta Zeros Data,
Completeness of Sato-Tate Group Data,
Completeness of Sato-Tate group data,
Completeness of data for families of higher genus curves with automorphisms,
Completeness of elliptic curve data,
Completeness of elliptic curve data over $\Q$,
Completeness of genus 2 curve data,
Completeness of the modular curve database,
Complex embedding,
Complex multiplication,
Complex multiplication,
Component group of a Sato-Tate group,
Components of a Sato-Tate group,
Conditional Mordell-Weil group,
Conductor,
Conductor of a Dirichlet character,
Conductor of a Dirichlet character from its Conrey label,
Conductor of a genus 2 curve,
Conductor of an Artin representation,
Conductor of an abelian variety,
Conductor of an elliptic curve,
Congruence subgroup,
Conjugacy classes,
Connected Sato-Tate group,
Conrey index of a Dirichlet character,
Conrey label of Dirichlet characters,
Contains $-I$,
Cusp orbits,
Cusp widths,
Cuspidal modular form,
Cusps of a modular curve,
Cyclic trigonal curve,
Data for a Galois orbit of Dirichlet characters,
Data for a dirichlet character,
Decomposition of the Jacobian of a genus 2 curve,
Dedekind domain,
Defining polynomial of a local field,
Degree of a Dirichlet character,
Degree of a Sato-Tate group,
Degree of a Siegel modular form,
Degree of a point on a modular curve,
Description of completeness,
Dimension,
Dimension,
Dimension,
Dimension,
Dimension of a family of curves,
Dirichlet L-function,
Dirichlet character,
Dirichlet character data extent,
Dirichlet character group,
Discriminant exponent of a local field,
Discriminant of a Weierstrass equation,
Discriminant of a genus 2 curve,
Distinguishing Hecke operators,
Divisor function,
Dual cuspform,
Dual pair of algebras,
Elliptic curve associated to a rational point,
Elliptic curve invariants,
Elliptic curve invariants,
Elliptic curve over a field,
Embedding Format,
Embedding of a Sato-Tate group,
Embedding of a modular form,
Embedding of a number field,
Endomorphism algebra,
Endomorphism algebra,
Endomorphism invariants,
Endomorphism lattice,
Endomorphism ring,
Endomorphism ring of an elliptic curve,
Endomorphism ring of an elliptic curve,
Euler factors at bad primes,
Euler product of an L-function,
Event probabilities,
Exceptional subgroup,
Extent of data for elliptic curves over $\Q$,
Extent of data for families of higher genus curves with automorphisms,
Extent of elliptic curve data over number fields,
Fiber product,
Field of values of a Dirichlet character,
Fields,
Find Hilbert modular form by label,
Find a Belyi map,
Find a Bianchi modular form,
Find a Dirichlet character,
Find a Galois group,
Find a Sato-Tate group,
Find a family of higher genus curves,
Find a genus 2 curve,
Find a hypergeometric motive,
Find a newform or newspace by label,
Find a number field,
Find a p-adic field,
Find an Artin representation,
Find an elliptic curve,
Find an elliptic curve,
Find an integral lattice,
Find an isogeny class of abelian varieties,
First $a_2$ moment,
Fourier coefficients of a modular form,
Fourier-Bessel expansion,
Fourth trace moment,
Fricke involution,
Frobenius matrix,
Frobenius order,
Frobenius prime,
Frobenius trace,
Full group of automorphisms,
Function fields of class number 1,
Functional equation of an L-function,
G2-invariants of a genus 2 curve,
GL2 subgroup data,
Galois conjugate newforms,
Galois invariants of a local field,
Galois orbit label,
Galois orbit of a Dirichlet character,
Galois orbit of a newform,
Galois representation,
Galois representations attached to an elliptic curve,
Galois representations attached to the Jacobian of a genus 2 curve,
Galois splitting model of a local field,
Gamma factors,
Gassmann class,
Gassmann equivalence,
Generating Frobenius classes,
Generating Vector,
Generators of a Sato-Tate group,
Genus 2 curve,
Genus of a modular curve,
Genus of a smooth curve ,
Genus of a subgroup of $\GL_2$,
Genus of a subgroup of the modular group,
Genus-rank difference,
Geometric automorphism group,
Geometric endomorphism algebra,
Geometric endomorphism ring,
Geometric isomorphism class of a curve,
Geometrically simple,
Global period of an elliptic curve,
Gonality of a curve,
Group algebra decomposition of Jacobian varieties ,
Groups,
Guidelines for writing annotations,
Half-integral weight modular forms,
Has square Ш,
Hasse-Weil conjecture,
Hecke characteristic polynomial,
Hecke kernel,
Hecke operator,
Hilbert modular surfaces source,
Hodge circle,
Holomorphic Eisenstein series of level 1,
How to cite genus 2 curves,
How to cite the LMFDB,
How zeros of the Riemann zeta function were computed,
Hyperbolic 3-space,
Hyperelliptic curve,
Ideal class group of a number field,
Ideal labels,
Identity component of a Sato-Tate group,
Igusa invariants of a genus 2 curve,
Igusa-Clebsch invariants of a genus 2 curve,
Image,
Image of $\ell$-adic Galois representation,
Image of mod-$\ell$ Galois representation,
Image of the adelic Galois representation,
Index of a modular curve,
Index of an open subgroup,
Index of the identity component,
Index of the image of a mod-$\ell$ Galois representation,
Index page, first sentences,
Induced Dirichlet character,
Infinity factor of an L-function,
Inner twist,
Inner twist count,
Inner twist group,
Inner twist multiplicity,
Inner twist proved,
Integral domain,
Introduction,
Introduction/Features,
Invariants of a genus 2 curve,
Invariants of a modular curve,
Invariants of an L-function,
Irreducible element,
Irreducible variety,
Isogeny between elliptic curves ,
Isogeny class degree,
Isogeny class of an abelian variety,
Isogeny decomposition of the Jacobian of a modular curve,
Isogeny of abelian varieties,
Isolated point on a modular curve,
Jacobi forms,
Jacobian of a curve,
Jacobian of a genus 2 curve,
Knowl,
Knowl Edit Guidelines,
Known points,
Known rational points,
L-function,
L-function of a classical modular form,
L-function of an abelian variety over $\mathbb{Q}$,
L-function spectral parameters ,
LMFDB Press,
Label for a $p$-adic field,
Label of a Galois orbit of a Dirichlet character,
Label of a classical modular form,
Label of a genus 2 curve over $\Q$,
Label of a modular curve,
Label of a subgroup $\GL_2(\widehat\mathbb Z)$,
Label search,
Labeling convention for families of higher genus curves,
Labels for Galois orbits of Dirichlet Characters,
Labels for the small group database in GAP and Magma,
Labels of elliptic curves over number fields,
Labels of mod-$\ell$ Galois representations,
Lattice additional acknowledgments,
Leading coefficient,
Level of a Bianchi modular form,
Level of a modular curve,
Level of a modular form,
Level of an open subgroup,
Level structure of a modular curve,
Local L-factors at good primes,
Local field,
Local field invariants,
Local invariants,
Local obstruction,
Locally solvable,
LuCaNT Conference,
Maass form coefficients,
Maass form on GL2(R) with trivial character,
Management board,
Matrix group,
Maximal $\ell$-adic Galois representation,
Maximal Galois representation,
Maximal ideal of a local field,
Maximal newform,
Maximal subgroups,
Minimal Dirichlet character,
Minimal Weierstrass equation over $\mathbb Q$,
Minimal equation of a hyperelliptic curve,
Minimal field of definition,
Minimal sibling,
Minimal supergroups,
Minimal twists of elliptic curves over $\mathbb{Q}$,
Minus space,
Mod-$\ell$ Galois image of a genus 2 curve,
Mod-$\ell$ Galois representation,
Modular Forms,
Modular cover,
Modular curve,
Modular curve $X(N)$,
Modular curve $X_{\text{ns}}^{+}(N)$,
Modular curve models,
Modular group $\mathrm {SL}(2,\mathbb Z)$,
Moment matrix,
Moment simplex,
Moment statistics,
Monodromy Group,
Mordell-Weil generator,
Mordell-Weil generators,
Mordell-Weil group,
Mordell-Weil group of an abelian variety,
Mordell-Weil rank,
Motives,
Motivic weight,
Multiplicative arithmetic function,
Multiplicity of an eigenvalue,
Name of a Sato-Tate group,
New subspace,
Newform,
Newform level of a modular form,
Newform subspace,
Newton polygon of a polynomial,
Nk^2,
Non rational low degree point,
Non-split Cartan subgroup,
Nonmaximal primes associated to genus $2$ curve,
Nontrivial inner twist,
Normalization of an L-function,
Normalizer of a Cartan subgroup,
Normalizer of a non-split Cartan subgroup,
Normalizer of a split Cartan subgroup,
Number fields related to a Dirichlet character,
Number of models,
Number of rational points,
Old subspace of modular forms,
Open subgroup,
Orbit index of a Dirichlet character,
Order of a Dirichlet character,
Order of a Dirichlet character from its label,
Order of a Mordell-Weil generator,
Order of a group,
Order of a group element,
Order of the image of a mod-$\ell$ Galois representation,
Other labels for modular curves,
Paramodular conjecture,
Paramodular newform,
Parity of a Dirichlet character,
Parity of a Dirichlet character from its Conrey label,
Parity of a representation,
Place of a number field,
Plane model,
Plane model,
Plus space,
Poincaré series,
Poincaré series,
Prime of a number field,
Prime of bad reduction,
Primes of good reduction,
Primitive Dirichlet character,
Principal Dirichlet character,
Principal homogeneous space,
Profinite group,
Projective field,
Projective image,
Quasi-modular form,
Quotient curve,
Quotient genus,
Ramified (rational) prime of a number field,
Rational L-function,
Rational Sato-Tate group,
Rational points,
Rational points on a modular curve,
Real dimension of a Sato-Tate group,
Real embedding,
Real endomorphism algebra,
Real multiplication,
Real multiplication,
Reduction of an elliptic curve,
Refined passport,
Relative dimension,
Release notes for version 1.3,
Reliability of Belyi map data,
Reliability of Bianchi modular form data,
Reliability of Curve L-function Data,
Reliability of Dirichlet L-function Data,
Reliability of Dynamically Computed L-function Data,
Reliability of Elliptic Curve L-function Data,
Reliability of Genus 2 Curve Data,
Reliability of Hilbert modular form data,
Reliability of L-function data,
Reliability of Maass form L-function data,
Reliability of Maass forms data,
Reliability of Modular L-function Data,
Reliability of Riemann Zeta Zeros Data,
Reliability of Sato-Tate Group Data,
Reliability of elliptic curve data,
Reliability of elliptic curve data over $\Q$,
Reliability of hypergeometric motive data,
Reliability of lattice data,
Reliability of mod-$\ell$ Galois representation data,
Reliability of modular curve data,
Reliability of the Classical Modular Form Data,
Reliability of the elliptic curve data,
Reliability of the higher genus curves with automorphisms data,
Representation,
Residue field,
Residue field degree of a local field,
Residue field of a point on a modular curve,
Riemann surface,
Riemann zeta-function,
Ring of integers of a local field,
Roadmap for Maass forms,
Rouse label,
Sage Mathematical Software System,
Sage cell server,
Satake parameters,
Sato-Tate group,
Sato-Tate group data,
Sato-Tate group identity component,
Sato-Tate group invariants,
Sato-Tate group labels,
Sato-Tate group of a genus 2 curve over Q,
Sato-Tate group of a modular form,
Sato-Tate subgroups and supergroups,
Search,
Searching on Galois images,
Second trace moment,
Selberg class of L-functions,
Selberg data for the functional equation of an L-function,
Self dual modular form,
Self twist field,
Self twist of a modular form,
Self-twist,
Separable algebra,
Sibling fields and algebras,
Siblings for a Galois group,
Siegel modular form,
Sign of a Bianchi newform,
Sign of the functional equation,
Signature of a group action on a curve,
Signature of a number field,
Simple,
Simple modular curve,
Simplified equation,
Simplified equation,
Slope content of a $p$-adic field,
Slopes of the Newton polygon of a polynomial,
Solvable,
Sort order,
Source of Bianchi modular form data,
Source of Classical Modular Forms Data,
Source of Dirichlet L-function Data,
Source of Dirichlet character data,
Source of Dynamically Computed L-function Data,
Source of Elliptic Curve L-function Data,
Source of Genus 2 Curve Data,
Source of Hilbert modular form data,
Source of L-function Data,
Source of L-function data,
Source of Maass form L-function Data,
Source of Maass forms data,
Source of Modular L-function Data,
Source of Riemann Zeta Zeros Data,
Source of Sato-Tate Group Data,
Source of Sato-Tate group data,
Source of elliptic curve data,
Source of elliptic curve data over $\Q$,
Source of elliptic curve data over $\Q$,
Source of elliptic curve data over number fields,
Source of global number field data,
Source of higher genus curves with automorphisms data,
Source of isogeny classes of abelian varieties over finite fields,
Source of mod-$\ell$ Galois representation data,
Source of modular curve data,
Source of p-adic field data,
Source of the higher genus curves with automorphisms data,
Source, reliability, and completeness,
Space of newforms,
Spaces of modular forms,
Split Cartan subgroup,
Splitting field of a mod-$\ell$ Galois representation,
Standard generators,
Standard modular curves,
Standard modular curves,
Sturm bound,
Sturm bound for $\Gamma_1(N)$,
Subspaces of modular forms,
Surjective,
Sylow subgroup,
Symplectic form,
Tamagawa number,
Tamagawa numbers,
Tame degree of a local field extension,
Tate-Shafarevich group,
Taxonomy of L-functions,
Test knowl suggestions,
The eigenvalue of a Maass form,
The ring of Siegel modular forms of degree 2 for $\Gamma(2)$,
The ring of Siegel modular forms of degree 2 for $\Gamma_0(2)$,
The ring of Siegel modular forms of degree 2 with respect to $\Gamma_0(3)$,
The ring of Siegel modular forms of degree 2 with respect to $\Gamma_0(3)$ with character $\psi_3$,
The ring of Siegel modular forms of degree 2 with respect to $\Gamma_0(4)$,
The ring of Siegel modular forms of degree 2 with respect to $\Gamma_0(4)$ with character,
The ring of Siegel modular forms of degree 2 with respect to the full modular group,
The ring of Siegel modular forms of degree 3 with respect to the full modular group,
The ring of Siegel modular forms of degree 4 with respect to the full modular group,
The ring of paramodular cusp forms $S_k(K(p))$,
Too many zeros,
Top slope,
Top slope for a local field,
Torsion group,
Torsion order,
Torsion subgroup,
Totally imaginary,
Trace bound,
Trace form,
Trace form,
Trace moments of a Sato-Tate group,
Trace zero density of a Sato-Tate group,
Transitive group name conventions,
Trivial zeros of an L-function,
Twin sextic algebra,
Twist,
Twist minimal,
Twist multiplicity,
Unit group torsion,
Unit in a ring,
Unitary symplectic group,
Unramified degree of a local field,
Unramified prime,
Upper half-plane,
Values of a Dirichlet character,
Values of a Dirichlet character on generators,
Vector valued Siegel modular forms of degree 2 taking values in three-dimensional space,
Weak equivalence class,
Weierstrass equation or model,
Weierstrass points of a hyperelliptic curve,
Weight $k$ slash-action,
Weight 2 Bianchi modular forms,
Weight of a Sato-Tate group,
Width of a cusp,
Wild inertia group,
Z-function of an L-function,
Zeros of an L-function,
cmf.minimal_twist,
group ring,
j-invariant of a rational elliptic curve,
j-invariant of an elliptic curve,
permutation module,
q-expansion of a modular form,
test,
test