On non-congruent numbers with 1 modulo 4 prime factors  

作　　者：OUYANG Yi ZHANG ShenXing 

机构地区：[1]Wu Wen-Tsun Key Laboratory of Mathematics, School of Mathematical Sciences, University of Science and Technology of China

出　　处：《Science China Mathematics》2014年第3期649-658,共10页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.11171317);National Key Basic Research Program of China(Grant No.2013CB834202)

摘　　要：In this paper, we use the 2-descent method to find a series of odd non-congruent numbers = 1 （nmd 8） whose prime factors are = 1 （rood 4） such that the congruent elliptic curves have second lowest Selmer groups, which include Li and Tian＇s result as special cases.In this paper,we use the 2-descent method to find a series of odd non-congruent numbers≡1(mod 8)whose prime factors are≡1(mod 4)such that the congruent elliptic curves have second lowest Selmer groups,which include Li and Tian’s result as special cases.

关 键 词：non-congruent number 2-descent second 2-descent 

分 类 号：O156[理学—数学]