On non-congruent numbers with 1 modulo 4 prime factors

Abstract

In this paper, we use the 2-decent method to find a series of odd non-congruent numbers $\equiv 1(\mathrm{mod}8)$ whose prime factors are $\equiv 1(\mathrm{mod}4)$ such that the congruent elliptic curves have second lowest Selmer groups, which includes Li and Tian's result (Li and Tian, 2000) as special cases.

References in corpus (1)

• The Birch-Swinnerton-Dyer Conjecture