Some new families of non-congruent numbers.

Abstract We construct several new families of non-congruent numbers with arbitrarily many prime factors congruent to 3 modulo 8. Our results generalize the work of Reinholz, Spearman and Yang [14]. Our methods are based on Monsky's formula on the 2-Selmer rank of the congruent elliptic curve and the recent results by Tian, Yuan and Zhang on the congruent number problem. [ABSTRACT FROM AUTHOR]