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.
Keywords:
so called second descent method several series non congruent numbers consider three different isogenies congruent elliptic curves their duals necessary condition estimate size images selmer groups selmer groups isogeny
Affiliations des auteurs :
Yi Ouyang
1
;
Shenxing Zhang
1
1
Wu Wen-Tsun Key Laboratory of Mathematics School of Mathematical Sciences University of Science and Technology of China Hefei, Anhui 230026, China
@article{10_4064_aa170_4_3,
author = {Yi Ouyang and Shenxing Zhang},
title = {On second 2-descent and non-congruent numbers},
journal = {Acta Arithmetica},
pages = {343--360},
year = {2015},
volume = {170},
number = {4},
doi = {10.4064/aa170-4-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/aa170-4-3/}
}
TY - JOUR
AU - Yi Ouyang
AU - Shenxing Zhang
TI - On second 2-descent and non-congruent numbers
JO - Acta Arithmetica
PY - 2015
SP - 343
EP - 360
VL - 170
IS - 4
UR - http://geodesic.mathdoc.fr/articles/10.4064/aa170-4-3/
DO - 10.4064/aa170-4-3
LA - en
ID - 10_4064_aa170_4_3
ER -
%0 Journal Article
%A Yi Ouyang
%A Shenxing Zhang
%T On second 2-descent and non-congruent numbers
%J Acta Arithmetica
%D 2015
%P 343-360
%V 170
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4064/aa170-4-3/
%R 10.4064/aa170-4-3
%G en
%F 10_4064_aa170_4_3
Yi Ouyang; Shenxing Zhang. On second 2-descent and non-congruent numbers. Acta Arithmetica, Tome 170 (2015) no. 4, pp. 343-360. doi: 10.4064/aa170-4-3
