大秩与小 conductor 的椭圆曲线
数论
2007-05-23 v3
摘要
对 r=6,7,...,11,我们找到了一条椭圆曲线 E/Q,其秩至少为 r 且 conductor 为已知最小者,相对先前纪录的改进因子从 1.0136(r=6)到超过 100(r=10 与 r=11)不等。我们描述了搜索方法,并列表给出对每个 r=5,6,...,11,我们所找到的 conductor 最低的五条曲线,以及(除 r=11 外)绝对值判别式最小的五条曲线。
引用
@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}
}
备注
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