Elliptic curves with few bad primes

被引：0

作者：

Wong, Siman ^{[1
]}

机构：

[1] Univ Massachusetts, Dept Math & Stat, Amherst, MA 01003 USA

来源：

INTERNATIONAL JOURNAL OF NUMBER THEORY | 2023年 / 19卷 / 01期

关键词：

Elliptic curves; semistable; Mordell-Weil rank; almost-prime; weighted sieve;

D O I：

10.1142/S1793042123500033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that there are >> X-1/2/log X semistable elliptic curves over Q with conductor <= X and at most two bad primes, and that there are >> X-1/6/log(3)X semistable elliptic curves over Q with conductor <= X, at most 12 bad primes, and positive Mordell-Weil rank. We also show that there are >> X-2/3/log X elliptic curves over Q with conductor 3(4)p for some prime p.

引用

页码：59 / 69

页数：11

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