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.
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页码：1501 / 1538
页数：38
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