On second 2-descent and non-congruent numbers
Volume 170 / 2015
Acta Arithmetica 170 (2015), 343-360
MSC: Primary 11G05; Secondary 11D25.
DOI: 10.4064/aa170-4-3
Abstract
We use the so-called second $2$-descent method to find several series of non-congruent numbers. We consider three different $2$-isogenies of the congruent elliptic curves and their duals, and find a necessary condition to estimate the size of the images of the $2$-Selmer groups in the Selmer groups of the isogeny.
