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# Wydawnictwa / Czasopisma IMPAN / Acta Arithmetica / Wszystkie zeszyty

## On second 2-descent and non-congruent numbers

### Tom 170 / 2015

Acta Arithmetica 170 (2015), 343-360 MSC: Primary 11G05; Secondary 11D25. DOI: 10.4064/aa170-4-3

#### Streszczenie

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.

#### Autorzy

• Yi OuyangWu Wen-Tsun Key Laboratory of Mathematics
School of Mathematical Sciences
University of Science and Technology of China
Hefei, Anhui 230026, China
e-mail
• Shenxing ZhangWu Wen-Tsun Key Laboratory of Mathematics
School of Mathematical Sciences
University of Science and Technology of China
Hefei, Anhui 230026, China
e-mail

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