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.
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页码：59 / 69
页数：11
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