21 citations · 50 across the 6 of their papers we have counts for
6 papers
Torsion points on elliptic curves over number fields of small degree
Maarten Derickx, Sheldon Kamienny, William Stein +1
We determine the set of possible prime orders of -rational points on elliptic curves over number fields of degree , for , , , and .
Databases of elliptic curves ordered by height and distributions of Selmer groups and ranks
Jennifer S. Balakrishnan, Wei Ho, Nathan Kaplan +3
Most systematic tables of data associated to ranks of elliptic curves order the curves by conductor. Recent developments, led by work of Bhargava-Shankar studying the average sizes…
A p-adic analogue of the conjecture of Birch and Swinnerton-Dyer for modular abelian varieties
Jennifer S. Balakrishnan, J. Steffen Müller, William A. Stein
Mazur, Tate, and Teitelbaum gave a p-adic analogue of the Birch and Swinnerton-Dyer conjecture for elliptic curves. We provide a generalization of their conjecture in the good ordi…
On the generation of the coefficient field of a newform by a single Hecke eigenvalue
Koopa Tak-Lun Koo, William Stein, Gabor Wiese
Let f be a non-CM newform of weight k > 1. Let L be a subfield of the coefficient field of f. We completely settle the question of the density of the set of primes p such that the…
Explicit Heegner Points: Kolyvagin's Conjecture and Non-trivial Elements in the Shafarevich-Tate Group
Dimitar Jetchev, Kristin Lauter, William Stein
Kolyvagin used Heegner points to associate a system of cohomology classes to an elliptic curve over $\Q$ and conjectured that the system contains a non-trivial class. His conjectur…
Modular Parametrizations of Neumann-Setzer Elliptic Curves
William Stein, Mark Watkins
Suppose is a prime of the form for some integer , which we take to be 3 mod 4. Then there are two Neumann--Setzer elliptic curves and of prime conductor…