- ID: john.jones

## Knowls

John Jones has contributed to these Knowls:
$T$-number of a transitive group,
$\GL_2$-type,
$\mathbb{Q}$-curves,
$p$-adic completion of a number field,
$p$-adic field (local number field),
$p$-adic logarithm,
A list of not so secret urls that aren't advertized,
A tour of the Riemann zeta function,
Abelian group,
Abelian number field,
Abelian surface,
Abelianization,
About varieties,
Absolute Galois group,
Absolute discriminant of a number field,
Abstract group name,
Acknowledgments for Artin representations,
Acknowledgments for Galois groups,
Acknowledgments for number fields,
Acknowledgments for p-adic fields,
Additive reduction,
Algebraic variety ,
Almost simple group,
Analytic class number formula,
Analytic order of Ш,
Analytic order of Sha (numerical value),
Arithmetically equivalent fields,
Arithmetically equivalent siblings,
Artin representation (definition),
Artin stem field,
Associative binary operation,
Assuming GRH,
Autjugate subgroups,
Automorphism group of a field extension,
Automorphisms of a group,
Bad reduction of an elliptic curve at a prime,
Base change,
Binary operation,
Birch and Swinnerton-Dyer conjecture,
Birch and Swinnerton-Dyer invariants of an elliptic curve/$\mathbb{Q}$,
Bézout determinant,
Bézout matrix,
Bézout matrix of a hypergeometric motive,
CM number field,
Canonical defining polynomial for number fields,
Canonical height,
Center of a group,
Central quotient,
Central subgroup,
Centralizer of a subgroup,
Centralizer of a subgroup,
Character of a Maass form,
Character of a group representation,
Character table data,
Characteristic of a ring,
Characteristic subgroup,
Chief series of a group,
Classical modular form,
Commutative binary operation,
Commutator subgroup of a group,
Complement,
Completeness and extent of Artin representation data,
Completeness and extent of Galois group data,
Completeness and extent of global number field data,
Completeness and extent of local field data,
Completeness of Hilbert modular form data,
Completeness of data on hypergeometric motives,
Completeness of data on hypergeometric motives,
Completeness of elliptic curve data over $\Q$,
Complex multiplication,
Complex multiplication,
Conductor,
Conductor labels for elliptic curves,
Conductor of a Dirichlet character,
Conductor of an Artin representation,
Conductor of an abelian number field,
Conductor of an elliptic curve,
Conductor of an elliptic curve over $\Q$,
Conductor valuation,
Conjugacy class,
Conjugacy class representatives,
Containing permutation representation,
Core of a subgroup,
Coset of a subgroup,
Create a knowl,
Cremona label,
Cyclic group,
Data for a global number field,
Data for a local field,
Data on small group,
Dedekind domain,
Defining Polynomial of a Number Field,
Defining parameters of a hypergeometric motive,
Defining polynomial of a local field,
Definition of $\Q_p$,
Definition of group,
Definition of ring,
Degree,
Degree of a hypergeometric motive,
Degree of a local field extension,
Degree of a number field,
Derived series of a group,
Description field in knowls,
Determinant of an Artin representation,
Developers Guide,
Dicyclic group,
Dihedral group,
Direct product of groups,
Dirichlet character,
Dirichlet character associated with a 1-dimensional Artin representation,
Dirichlet character group,
Dirichlet group of an Abelian number field,
Discriminant exponent of a local field,
Discriminant of a Weierstrass equation,
Discriminant of a number field,
Discriminant of an elliptic curve over $\Q$,
Discriminant root field,
Discriminant root field of a local field,
Discriminant valuation,
Divisions of a group,
Dual cuspform,
Duke-Imamoglu-Ikeda lift,
Eisenstein polynomial,
Elementary group,
Elliptic curve invariants,
Elliptic curve invariants,
Elliptic curve over $\mathbb Q$ ,
Elliptic curve over a field,
Elusive group,
Endomorphism of an elliptic curve,
Endomorphism ring of an elliptic curve,
Endomorphism ring of an elliptic curve,
Euclidean domain,
Expand a knowl,
Exponent of a group,
Extent of Galois group data,
Extent of data for elliptic curves over $\Q$,
Extent of elliptic curve data over number fields,
Extent of global number field data,
Extent of local number field data,
Faithful representation,
Field,
Field automorphisms associated with a Galois group,
Field of fractions of an integral domain,
Find a Galois group,
Fitting subgroup of a group,
Fixed field of a Dirichlet character,
Fourier expansion of a Maass form on PSL(2,Z[i]),
Fractional ideal,
Frattini subgroup of a group,
Frobenius cycle types,
Frobenius-Schur indicator of a representation,
Fundamental domain of $\SL(2,\Z)$,
Fundamental units of a number field,
Galois closure of an extension,
Galois group,
Galois group,
Galois group information,
Galois group label,
Galois group of a number field -- naming convention,
Galois invariants of a local field,
Galois mean slope,
Galois module information,
Galois module structure of Type I (i) for units in biquadratic number fields,
Galois module structure of Type I (ii) for units in biquadratic number fields,
Galois module structure of Type I (iii) for units in biquadratic number fields,
Galois module structure of Type II (i) for units in biquadratic number fields,
Galois module structure of Type II (ii) for units in biquadratic number fields,
Galois module structure of Type III for units in biquadratic number fields,
Galois module structure of Type IV for units in biquadratic number fields,
Galois orbit,
Galois orbit of an Artin representation,
Galois representations attached to an elliptic curve,
Galois root discriminant,
Galois splitting model of a local field,
Gassmann equivalence,
Generalized Riemann hypothesis,
Generator of a number field,
Generators of a group,
Generators of permutation group,
Generic dynamic knowl,
Geometric endomorphism algebra,
Geometry type of a Belyi map,
Global minimal model,
Good ordinary reduction,
Good reduction,
Good supersingular reduction,
Gritsenko lift,
Group $\Gamma_0(N)$ subgroup of $\textrm{SL}(2,\mathbb{Z})$,
Group $\Gamma_1(N)$ subgroup of $\textrm{SL}(2,\mathbb{Z})$,
Group action Invariants,
Group homomorphism,
Group invariants,
Group isomorphism,
Groups,
Haar measure of a topological group,
Hall subgroup,
Has square Ш,
Hasse diagram,
Hecke character,
Hecke operators,
Hilbert modular form,
Hodge vector of a hypergeometric motive,
Hodge vector of a hypergeometric motive,
How zeros of the Riemann zeta function were computed,
Hyperelementary group,
Ideal class group of a number field,
Ideal of a ring,
Identifier of a knowl,
Identity for a binary operation,
Image of mod-$\ell$ Galois representation,
Image of the representation,
Implicit creation of knowls,
Imprimitivity index of a hypergeometric motive,
Imprimitivity index of a hypergeometric motive,
Indecomposable integral representation,
Index of a number field,
Index of a subgroup,
Index of an order,
Index page, first sentences,
Indices of inseparability,
Inertia group,
Inertia group searching,
Inessential prime,
Inner automorphism of a group,
Input for arithmetically equivalent fields,
Integral basis of a number field,
Integral domain,
Integral element of a ring,
Integral elements,
Integral model,
Integral points,
Integrally closed,
Intermediate fields,
Intermediate fields,
Inverse for a binary operation,
Is a Galois extension,
Isogeny between elliptic curves ,
Isogeny class of an elliptic curve,
Isogeny graph of an isogeny class of elliptic curves,
Isogeny matrix of an isogeny class of elliptic curves,
Isomorphism between Weierstrass models,
Isomorphism of elliptic curves,
Iwasawa invariants of elliptic curves,
Knowl Edit Guidelines,
Knowl with parameters,
Kodaira symbol,
Kodaira symbol,
Label for a $p$-adic field,
Label for an Artin representation,
Label for an elliptic curve over $\mathbb Q$,
Label of a hypergeometric motive,
Labels of elliptic curves over number fields,
Laplace-Beltrami operator (hyperbolic),
Level of a modular form,
Local algebra,
Local algebra,
Local data of an elliptic curve,
Local field,
Local field invariants,
Local minimal discriminant of an elliptic curve,
Local minimal model,
Local root number,
Lower central series of a group,
Maass form on GL2(R) with trivial character,
Maass forms on PSL(2,Z[i]),
Management board,
Maximal Galois representation,
Maximal ideal,
Maximal subgroup of a group,
Minimal Weierstrass equation over $\mathbb Q$,
Minimal discriminant,
Minimal modular form,
Minimal sibling,
Miyawaki lift ,
Modular degree of an elliptic curve over $\mathbb Q$,
Modular form associated to an elliptic curve/$\mathbb Q$,
Modular parametrization of an elliptic curve over $\mathbb Q$,
Modulus of a Dirichlet character,
Monogenic field,
Monomial group,
Mordell-Weil group,
Mordell-Weil theorem,
Multiplicative Galois Module Structure,
Multiplicative reduction,
Naming conventions for knowls,
Naming suggestions,
Newform,
Nilpotent group,
Noetherian ring,
Non-singular point (definition),
Non-split multiplicative reduction,
Norm of discriminant,
Normal closure of a subgroup,
Normal series of a group,
Normal subgroup of a group,
Normalization of defining polynomials for number fields,
Normalizer of a subgroup,
Number field,
Number field associated to an Artin representation,
Number field invariants,
Number field label,
Number field not in the database,
Number fields contributed by Noam Elkies,
Number fields related to a Dirichlet character,
Obstruction class of an elliptic curve,
Optimal elliptic curve over $\mathbb Q$,
Order of a Dirichlet character,
Order of a group,
Outer automorphism group,
Paramodular newform,
Parity of a Dirichlet character,
Parity of a Galois group,
Parity of a representation,
Permutation degree,
Place of a number field,
Power classes,
Presentation of a finite group,
Prime ideal,
Primitive Dirichlet character,
Primitivity of a Galois group,
Principal fractional ideal,
Principal ideal domain,
Projective Artin field,
Projective image of an Artin representation,
Projective image type,
Projective special linear group $\text{PSL}_2(\mathbb{R})$,
Projective stem field of an Artin representation,
Proper subgroup,
Quotient group,
Radical of a group,
Ramification index of a prime in a local field,
Ramification polygon,
Ramified (rational) prime of a number field,
Ramified prime of an Artin representation,
Rank of a number field,
Rank of an elliptic curve over a number field,
Rational character table of a group,
Real period,
Reduction type,
Reduction type of an elliptic curve over $\mathbb Q$,
Regulator of a number field,
Regulator of elliptic curve,
Reliability of Artin representation data,
Reliability of Dirichlet Character Data,
Reliability of Maass form L-function data,
Reliability of global number field data,
Reliability of local field data,
Reliability of transitive group data,
Residue field degree of a local field,
Resolvents of a Galois group,
Ring of integers of a number field,
Roadmap for L-functions,
Roadmap for Maass forms,
Roadmap for Siegel modular forms,
Roadmap for elliptic curves,
Roadmap for future areas of LMFBD,
Root discriminant of a number field,
Root number of a local field,
Rouse label,
Sage Mathematical Software System,
Sage cell knowl,
Saito-Kurokawa lift,
Searching $p$-adic completions of a number field,
Selberg class axioms,
Self dual modular form,
Semi-global minimal model,
Semidirect product of groups,
Separable extension,
Serre Odlyzko bound,
Sibling fields and algebras,
Siblings for a Galois group,
Siegel Eisenstein series,
Siegel Klingen-Eisenstein series,
Siegel cusp form,
Siegel modular form,
Siegel modular form with character,
Simple group name,
Simple groups,
Slope content of a $p$-adic field,
Socle of a group,
Solvable group,
Source of Artin representation data,
Source of Dirichlet character data,
Source of Hilbert modular form data,
Source of abstract group data,
Source of elliptic curve data over $\Q$,
Source of global number field data,
Source of hypergeometric data,
Source of hypergeometric data,
Source of p-adic field data,
Source of transitive group data,
Special value of an elliptic curve L-function,
Split and non-split extension of groups,
Split multiplicative reduction,
Stem field for a Galois extension,
Subfields,
Subgroup diagram,
Subgroup diagrams in the LMFDB,
Subgroup of a group,
Subnormal series,
Sylow subgroup,
Symmetric power of an L-function,
Tamagawa number,
Tamagawa numbers for an elliptic curve ,
Tame degree of a local field extension,
Tate module of an elliptic curve,
The unramified/totally ramified tower of a local field,
Top slope,
Top slope for a local field,
Torsion growth in number fields,
Torsion order of an elliptic curve,
Torsion subgroup of an elliptic curve,
Torsion subgroup of an elliptic curve over $\mathbb Q$,
Totally real,
Trace of complex conjugation,
Transformation property for modular forms,
Transitive degree,
Transitive group name conventions,
Trivial subgroup,
Twin sextic algebra,
Type of a complex group representation,
Type of groups ,
Underlying unit group for a Dirichlet character,
Unique factorization domain,
Unit group of a number field,
Unramified (rational) prime of a number field,
Unramified degree of a local field,
Unramified prime of an Artin representation,
Unramified subfield,
Upload data,
Upper central series of a group,
Vector-valued Siegel modular forms,
Visible slopes,
Weierstrass equation or model,
Weil height of a point on an elliptic curve over $\Q$,
Weyl group,
Wild inertia group,
Wild inertia group search,
Wild slopes of a local field,
Wreath product,
Zero divisor,
j-invariant denominator valuation,
j-invariant of a rational elliptic curve,
j-invariant of an elliptic curve,
lambda-invariant of an elliptic curve,
mu-invariant of an elliptic curve,
p-part of defining parameters of a hypergeometric motive,
prime to $p$-part of defining parameters of a hypergeometric motive