51 citations · 209 across the 18 of their papers we have counts for
19 papers
Computing the endomorphism ring of an elliptic curve over a number field
John E. Cremona, Andrew V. Sutherland
We describe deterministic and probabilistic algorithms to determine whether or not a given monic irreducible polynomial H in Z[X] is a Hilbert class polynomial, and if so, which on…
On the equivalence of binary cubic forms
J E Cremona
We consider the question of determining whether two binary cubic forms over an arbitrary field whose characteristic is not or are equivalent under the actions of either…
The density of polynomials of degree over having exactly roots in
Manjul Bhargava, John Cremona, Tom Fisher +1
We determine the probability that a random polynomial of degree over has exactly roots in , and show that it is given by a rational function of…
Sorting and labelling integral ideals in a number field
John Cremona, Aurel Page, Andrew V. Sutherland
We define a scheme for labelling and ordering integral ideals of number fields, including prime ideals as a special case. The order we define depends only on the choice of a monic…
The proportion of genus one curves over defined by a binary quartic that everywhere locally have a point
Manjul Bhargava, John Cremona, Tom Fisher
We consider the proportion of genus one curves over of the form where is a binary quartic form (or more generally of the form $…
Computing classical modular forms
Alex J. Best, Jonathan Bober, Andrew R. Booker +8
We discuss practical and some theoretical aspects of computing a database of classical modular forms in the L-functions and Modular Forms Database (LMFDB).
Global methods for the symplectic type of congruences between elliptic curves
John Cremona, Nuno Freitas
We describe a systematic investigation into the existence of congruences between the mod torsion modules of elliptic curves defined over , including methods to dete…
On rational Bianchi newforms and abelian surfaces with quaternionic multiplication
John Cremona, Lassina Dembélé, Ariel Pacetti +2
We study the rational Bianchi newforms (weight 2, trivial character, with rational Hecke eigenvalues) in the LMFDB that are not associated to elliptic curves, but instead to abelia…
On Elliptic Curves of prime power conductor over imaginary quadratic fields with class number one
John Cremona, Ariel Pacetti
The main result of this paper is to extend from $\Q$ to each of the nine imaginary quadratic fields of class number one a result of Serre (1987) and Mestre-Oesterlé (1989), namely…
Black Box Galois Representations
Alejandro Argáez-García, John Cremona
We develop methods to study -dimensional -adic Galois representations of the absolute Galois group of a number field , unramified outside a known finite set of primes…
The L-functions and modular forms database project
John Cremona
The Langlands Programme, formulated by Robert Langlands in the 1960s and since much developed and refined, is a web of interrelated theory and conjectures concerning many objects i…
The proportion of plane cubic curves over that everywhere locally have a point
Manjul Bhargava, John Cremona, Tom Fisher
We show that the proportion of plane cubic curves over that have a -rational point is a rational function in , where the rational function is inde…
What is the probability that a random integral quadratic form in variables is isotropic?
Manjul Bhargava, John Cremona, Tom Fisher
We show that the density of quadratic forms in variables over that are isotropic is a rational function in , where the rational function is independent of $p…
Tetrahedral Elliptic Curves and the local-global principle for Isogenies
Barinder Singh Banwait, John Cremona
We study the failure of a local-global principle for the existence of -isogenies for elliptic curves over number fields . Sutherland has shown that over there is…
Explicit n-descent on elliptic curves. III. Algorithms
John Cremona, Tom Fisher, Cathy O'Neil +2
This is the third in a series of papers in which we study the n-Selmer group of an elliptic curve, with the aim of representing its elements as curves of degree n in P^{n-1}. The m…
The complex AGM, periods of elliptic curves over C and complex elliptic logarithms
John E. Cremona, Thotsaphon Thongjunthug
We give an account of the complex Arithmetic-Geometric Mean (AGM), as first studied by Gauss, together with details of its relationship with the theory of elliptic curves over $\C$…
Minimisation and reduction of 2-, 3- and 4-coverings of elliptic curves
John Cremona, Tom Fisher, Michael Stoll
In this paper we consider models for genus one curves of degree n for n = 2, 3 and 4, which arise in explicit n-descent on elliptic curves. We prove theorems on the existence of mi…
Explicit n-descent on elliptic curves, II. Geometry
John Cremona, Tom Fisher, Cathy O'Neil +2
This is the second in a series of papers in which we study the n-Selmer group of an elliptic curve. In this paper, we show how to realize elements of the n-Selmer group explicitly…
Explicit n-descent on elliptic curves, I. Algebra
John Cremona, Tom Fisher, Cathy O'Neil +2
This is the first in a series of papers in which we study the n-Selmer group of an elliptic curve, with the aim of representing its elements as genus one normal curves of degree n.…