On elliptic curves with large Tate-Shafarevich groups

被引：7

作者：

Atake, D ^{[1
]}

机构：

[1] Kyoto Univ, Grad Sch Math, Kyoto 6068502, Japan

来源：

JOURNAL OF NUMBER THEORY | 2001年 / 87卷 / 02期

关键词：

elliptic curve; Tate Shafarevich group; quadratic field; quadratic residue symbol;

D O I：

10.1006/jnth.2000.2599

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Generalizing results of Lemmermeyer. we show that the 2-ranks of the Tate-Shafarevich groups of quadratic twists of certain elliptic curves with a rational point of order 2 can be arbitrarily large. We use only quadratic residue symbols in a quadratic field to obtain our results. (C) 2001 Academic Press.

引用

页码：282 / 300

页数：19

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