Infinite descent on elliptic curves

被引：50

作者：

Siksek, S ^{[1
]}

机构：

[1] UNIV EXETER, DEPT MATH, EXETER EX4 4QE, DEVON, ENGLAND

来源：

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS | 1995年 / 25卷 / 04期

关键词：

elliptic curves; Diophantine equations; computational number theory; Mordell-Weil group;

D O I：

10.1216/rmjm/1181072159

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present an algorithm for computing an upper bound for the difference of the logarithmic height and the canonical height on elliptic curves. Moreover, a new method for performing the infinite descent on elliptic curves is given, using ideas from the geometry of numbers. These algorithms are practical and are demonstrated by a few examples.

引用

页码：1501 / 1538

页数：38

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