We give some sufficient conditions for non-congruent numbers in terms of the Monsky matrices.Many known criteria for non-congruent numbers can be viewed as special cases of our results.
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, w...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.展开更多
基金supported by NSFC(Nos.12231009,11971224,12071209).
文摘We give some sufficient conditions for non-congruent numbers in terms of the Monsky matrices.Many known criteria for non-congruent numbers can be viewed as special cases of our results.
基金supported by National Natural Science Foundation of China(Grant No.11171317)National Key Basic Research Program of China(Grant No.2013CB834202)
文摘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.
