Torsion subgroups of elliptic curves in elementary abelian 2-extensions of Q

被引：22

作者：

Fujita, Y ^{[1
]}

机构：

[1] Tohoku Univ, Inst Math, Sendai, Miyagi 9808578, Japan

来源：

JOURNAL OF NUMBER THEORY | 2005年 / 114卷 / 01期

关键词：

elliptic curves; torsion subgroups;

D O I：

10.1016/j.jnt.2005.03.005

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let E be an elliptic curve over Q and let F: = Q({root m; m is an element of Z}). Laska and Lorenz showed that there exist at most 31 possibilities for the type of the torsion subgroup E(F)(tors) of E over F. In this paper, we showed that there exist exactly 20 possibilities for E(F)(tors). (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：124 / 134

页数：11