Elliptic curves of large rank and small conductor
Number Theory
2007-05-23 v3
Abstract
For r=6,7,...,11 we find an elliptic curve E/Q of rank at least r and the smallest conductor known, improving on the previous records by factors ranging from 1.0136 (for r=6) to over 100 (for r=10 and r=11). We describe our search methods, and tabulate, for each r=5,6,...,11, the five curves of lowest conductor, and (except for r=11) also the five of lowest absolute discriminant, that we found.
Cite
@article{arxiv.math/0403374,
title = {Elliptic curves of large rank and small conductor},
author = {Noam D. Elkies and Mark Watkins},
journal= {arXiv preprint arXiv:math/0403374},
year = {2007}
}
Comments
16 pages, including tables and one .eps figure; to appear in the Proceedings of ANTS-6 (June 2004, Burlington, VT). Revised somewhat after comments by J.Silverman on the previous draft, and again to get the correct page breaks