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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa170-4-3,
author = {Yi Ouyang and Shenxing Zhang},
title = {On second 2-descent and non-congruent numbers},
journal = {Acta Arithmetica},
volume = {168},
year = {2015},
pages = {343-360},
zbl = {06480403},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa170-4-3}
}
Yi Ouyang; Shenxing Zhang. On second 2-descent and non-congruent numbers. Acta Arithmetica, Tome 168 (2015) pp. 343-360. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa170-4-3/