Computing the rational torsion of an elliptic curve using tate normal form

被引：13

作者：

García-Selfa, I ^{[1
]}

Olalla, MA ^{[1
]}

Tornero, JM ^{[1
]}

机构：

[1] Univ Seville, Fac Matemat, E-41080 Seville, Spain

来源：

JOURNAL OF NUMBER THEORY | 2002年 / 96卷 / 01期

关键词：

elliptic curves; rational points;

D O I：

10.1006/jnth.2002.2780

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is a classical result (apparently due to Tate) that all elliptic curves with a torsion point of order n (4 less than or equal to n less than or equal to 10, or n = 12) lie in a one-parameter family. However, this fact does not appear to have been used ever for computing the torsion of an elliptic curve. We present here an extremely down-to-earth algorithm using the existence of such a family. (C) 2002 Elsevier Science (USA).

引用

页码：76 / 88

页数：13

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