On the elliptic curve y^2=x^3-2r Dx and factoring integers

作     者：LI XiuMei ZENG JinXiang 

作者机构：Department of Mathematical SciencesTsinghua University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2014年第57卷第4期

页      面：719-728页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No. 11271212) 

主　　题：elliptic curve integer factoring Selmer group 

摘      要：Let D=pq be the product of two distinct odd *** the parity conjecture,we construct infinitely many r≥1 such that E2rD:y2=x3-2rDx has conjectural rank one and vp(x([k]Q))≠vq(x([k]Q))for any odd integer k,where Q is the generator of the free part of E(Q).Furthermore,under the generalized Riemann hypothesis,the minimal value of r is less than c log4 D for some absolute constant *** a corollary,one can factor D by computing the generator Q.