On the elliptic curve y 2 = x 3-2rDx and factoring integers

被引：2

作者：

Li XiuMei ^{[1
]}

Zeng JinXiang ^{[1
]}

机构：

[1] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2014年 / 57卷 / 04期

基金：

中国国家自然科学基金;

关键词：

elliptic curve; integer factoring; Selmer group; POINTS;

D O I：

10.1007/s11425-014-4769-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let D = pq be the product of two distinct odd primes. Assuming the parity conjecture, we construct infinitely many r a (c) 3/4 1 such that E (2rD) : y (2) = x (3) -2rDx has conjectural rank one and v (p) (x([k]Q)) not equal v (q) (x([k]Q)) for any odd integer k, where Q is the generator of the free part of E(a"e). Furthermore, under the generalized Riemann hypothesis, the minimal value of r is less than c log(4) D for some absolute constant c. As a corollary, one can factor D by computing the generator Q.

引用

页码：719 / 728

页数：10