On second 2-descent and non-congruent numbers

Yi Ouyang, and Shenxing Zhang. "On second 2-descent and non-congruent numbers." Acta Arithmetica 170.4 (2015): 343-360. <http://eudml.org/doc/279543>.

@article{YiOuyang2015,
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.},
author = {Yi Ouyang, Shenxing Zhang},
journal = {Acta Arithmetica},
keywords = {non-congruent number; 2-descent},
language = {eng},
number = {4},
pages = {343-360},
title = {On second 2-descent and non-congruent numbers},
url = {http://eudml.org/doc/279543},
volume = {170},
year = {2015},
}

TY - JOUR
AU - Yi Ouyang
AU - Shenxing Zhang
TI - On second 2-descent and non-congruent numbers
JO - Acta Arithmetica
PY - 2015
VL - 170
IS - 4
SP - 343
EP - 360
AB - 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.
LA - eng
KW - non-congruent number; 2-descent
UR - http://eudml.org/doc/279543
ER -