Geodesic
On second 2-descent and non-congruent numbers
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
Acta Arithmetica, Tome 170 (2015) no. 4, pp. 343-360 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/aa170-4-3
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

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 
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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

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