- ID: cremona

## Knowls

John Cremona has contributed to these Knowls:
,
$\GL_2$-type,
$\PSL_2$-index,
$\mathbb{Q}$-curves,
$p$-adic field (local number field),
2-Selmer rank,
A list of not so secret urls that aren't advertized,
Absolute Galois group,
Absolute discriminant,
Absolute value of a field,
Absolutely irreducible,
Acknowledgments for Bianchi modular forms,
Acknowledgments for elliptic curves over $\Q$,
Acknowledgments for elliptic curves over number fields,
Acknowledgments for hosting,
Additive reduction,
Affine space,
Algebraic closure of a field,
Algebraic curve,
Algebraic variety ,
Alternating group,
Analytic conductor of a classical newform,
Analytic order of Ш,
Analytic order of Ш,
Analytic order of Sha (numerical value),
Analytic rank of a Bianchi newform,
Analytic rank of a curve,
Analytic rank of an elliptic curve over $\Q$,
Arithmetic L-function,
Automorphism group of a field extension,
Automorphism group of an algebraic curve,
Bad reduction of an elliptic curve at a prime,
Base change,
Base-change Bianchi modular forms,
Bianchi modular form,
Bianchi modular forms,
Bianchi newform,
Birch Swinnerton-Dyer conjecture,
Birch and Swinnerton-Dyer conjecture,
Birch and Swinnerton-Dyer invariants of an elliptic curve/$\mathbb{Q}$,
CM Bianchi newforms,
CM form,
Canonical defining polynomial for number fields,
Canonical height,
Canonical height on an elliptic curve,
Characteristic polynomial of Frobenius,
Classical modular form,
Codomain,
Completeness of Bianchi Modular Form data,
Completeness of Bianchi modular form data,
Completeness of Hilbert modular form data,
Completeness of L-function Data,
Completeness of elliptic curve data,
Completeness of elliptic curve data over $\Q$,
Completeness of genus 2 curve data,
Complex embedding,
Complex multiplication,
Complex multiplication,
Conductor,
Conductor labels for elliptic curves,
Conductor of an elliptic curve,
Conductor of an elliptic curve over $\Q$,
Conductor valuation,
Congruent number curves,
Congruent number problem,
Congruent numbers,
Conrey label of Dirichlet characters,
Cremona label,
Data for a local field,
Decomposition of the Jacobian of a genus 2 curve,
Defining Polynomial of a Number Field,
Defining polynomial of a local field,
Definition of $\Q_p$,
Degree of a local field extension,
Dimension,
Dimension of a Hecke orbit,
Dirichlet character,
Dirichlet character group,
Discriminant exponent of a local field,
Discriminant of a Weierstrass equation,
Discriminant of a genus 2 curve,
Discriminant of an elliptic curve over $\Q$,
Discriminant root field of a local field,
Discriminant valuation,
Elliptic curve invariants,
Elliptic curve invariants,
Elliptic curve over a field,
Embedding of a number field,
Endomorphism invariants,
Endomorphism lattice,
Endomorphism of an elliptic curve,
Endomorphism ring,
Endomorphism ring of an elliptic curve,
Endomorphism ring of an elliptic curve,
Euler factors at bad primes,
Extent of data for elliptic curves over $\Q$,
Extent of elliptic curve data over number fields,
Extent of local number field data,
Faltings height of an elliptic curve,
Faltings ratio,
Find a Bianchi modular form,
Fixed field of a Dirichlet character,
Frobenius order,
Frobenius trace,
Further extent of the data on isogeny classes of abelian varieties over finite fields,
G2-invariants of a genus 2 curve,
Galois invariants of a local field,
Galois orbit of a Dirichlet character,
Gamma factors,
Generating Frobenius classes,
Generator of a number field,
Genus 2 curve,
Geometric automorphism group,
Geometric isomorphism class of a curve,
Global minimal model,
Global period of an elliptic curve,
Good ordinary reduction,
Good reduction,
Good supersingular reduction,
Has square Ш,
Hecke algebra,
Hilbert modular form,
Hyperbolic 3-space,
Ideal labels,
Ideal of a ring,
Igusa invariants of a genus 2 curve,
Igusa-Clebsch invariants of a genus 2 curve,
Image,
Image of mod-$\ell$ Galois representation,
Index of an order,
Index of the image of a mod-$\ell$ Galois representation,
Integral elements,
Integral model,
Integral points,
Intermediate fields,
Invariants of a genus 2 curve,
Isogeny between elliptic curves ,
Isogeny class of an abelian variety,
Isogeny class of an elliptic curve,
Isomorphism between Weierstrass models,
Isomorphism of elliptic curves,
Iwasawa invariants of elliptic curves,
Jacobian of a genus 2 curve,
Knowl Edit Guidelines,
Known rational points,
Kodaira symbol,
Kronecker symbol,
L-function of an abelian variety over $\mathbb{Q}$,
LMFDB Press,
Label for a $p$-adic field,
Label for an elliptic curve over $\mathbb Q$,
Label of a Galois orbit of a Dirichlet character,
Label of a genus 2 curve over $\Q$,
Labels of Bianchi modular forms,
Labels of elliptic curves over number fields,
Level of a Bianchi modular form,
Local L-factors at good primes,
Local algebra,
Local data of an elliptic curve,
Local field invariants,
Local invariants,
Local minimal discriminant of an elliptic curve,
Local minimal model,
Local root number,
Locally solvable,
Maass form plot,
Manin constant for elliptic curves over $\Q$,
Maximal Galois representation,
Minimal Weierstrass equation over $\mathbb Q$,
Minimal discriminant,
Minimal polynomial,
Minimal twists of elliptic curves over $\mathbb{Q}$,
Mod-$\ell$ Galois representation,
Modular Forms,
Monomial order,
Mordell-Weil group,
Mordell-Weil rank,
Mordell-Weil theorem,
Multiplicative reduction,
Narrow class group,
Narrow class number,
Newton polygon of a polynomial,
Non-split multiplicative reduction,
Norm of discriminant,
Number field associated to an Artin representation,
Number fields related to a Dirichlet character,
Number of rational points,
Obstruction class of an elliptic curve,
Optimal elliptic curve over $\mathbb Q$,
Order,
Order of a Dirichlet character from its label,
Order of a group element,
Order of the image of a mod-$\ell$ Galois representation,
Parity of a Galois group,
Period lattice of an elliptic curve,
Pictures for elliptic curves over $\mathbb{Q}$,
Potential good reduction,
Primes of good reduction,
Primitive element,
Projective space,
Ramification index of a prime in a local field,
Ramified primes of a mod-$\ell$ Galois representation,
Rank of an elliptic curve over a number field,
Rational points,
Real period,
Reduction type,
Reduction type of an elliptic curve over $\mathbb Q$,
Reflex field,
Regulator of an elliptic curve,
Regulator of elliptic curve,
Related objects,
Reliability of Bianchi Modular Form data,
Reliability of elliptic curve data,
Reliability of elliptic curve data over number fields,
Reliability of the elliptic curve data,
Residue field degree of a local field,
Roadmap for elliptic curves,
Roadmap for future areas of LMFBD,
Roadmap for local number fields,
Root number of a local field,
Rouse label,
Sato-Tate group identity component,
Sato-Tate group labels,
Sato-Tate group of a genus 2 curve over Q,
Self-dual L-function,
Self-twist,
Semi-global minimal model,
Sign of a Bianchi newform,
Slope content of a $p$-adic field,
Slopes of the Newton polygon of a polynomial,
Solvable,
Source of Bianchi modular form data,
Source of Bianchi modular form data,
Source of Genus 2 Curve Data,
Source of elliptic curve data,
Source of elliptic curve data over $\Q$,
Source of elliptic curve data over number fields,
Spaces of Bianchi modular forms,
Split multiplicative reduction,
Splitting field of a mod-$\ell$ Galois representation,
Surjective,
Tamagawa number,
Tamagawa numbers,
Tate module of an elliptic curve,
The unramified/totally ramified tower of a local field,
Too many zeros,
Top slope for a local field,
Torsion growth in number fields,
Torsion order,
Torsion order of an elliptic curve,
Torsion subgroup,
Torsion subgroup of an elliptic curve,
Torsion subgroup of an elliptic curve over $\mathbb Q$,
Totally imaginary,
Twists of elliptic curves,
Upper half-plane,
Weierstrass equation or model,
Weierstrass points of a hyperelliptic curve,
Weight of a Bianchi modular form,
Weil height of a point on an elliptic curve over $\Q$,
j-invariant denominator valuation,
j-invariant of an elliptic curve,
lambda-invariant of an elliptic curve,
mu-invariant of an elliptic curve