On second 2-descent and non-congruent numbers

• Autorzy: Yi Ouyang , Shenxing Zhang
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11D25: Cubic and quartic equations
• 11G05: Elliptic curves over global fields

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2015
• Tom: 170
• Numer: 4
• Strony: 343-360

Daty

wydano

2015

Twórcy

autor

Yi Ouyang

• Wu Wen-Tsun Key Laboratory of Mathematics, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China

autor

Shenxing Zhang

• Wu Wen-Tsun Key Laboratory of Mathematics, School of Mathematical Sciences, University of Science and Technology of China, Hefei, Anhui 230026, China

Identyfikatory

DOI

10.4064/aa170-4-3