Computational verification of the Birch and Swinnerton-Dyer conjecture for individual elliptic curves

by G. Grigorov, A. Jorza, S. Patrikis, C. Tarnita, and W. Stein

Published Version in Math. Comp. 2009


We describe theorems and computational methods for verifying the Birch and Swinnerton-Dyer conjecture for specific elliptic curves over Q. We apply our techniques to show that if E is a non-CM elliptic curve over Q of conductor ≤ 1000 and rank ≤ 1, then the full Birch and Swinnerton-Dyer conjecture is true for E up to odd primes that divide either a Tamagawa number of E or the degree of some rational cyclic isogeny with domain E.

Lawson and Wuthrich's 2015 paper addresses a serious mistake in Lemma 5.4 of this paper.
PDF Notes and mp3 audio from 2005-07-11 Bremen talk

Download the Paper
LaTeX Source
Relevant Data, Tables, and Programs