Author(s)： Shun'ichi Yokoyama and Yu Shimasaki

J. Math-for-Ind. 3B (2011) 113-117.

• File： JMI2011B-4.pdf (120KB)

Abstract
We prove the non-existence of elliptic curves having good reduction everywhere over some real quadratic fields. These results of computations give best-possible data including structures of Mordell-Weil groups over real quadratic fields $\mathbb{Q}(\sqrt{m})$ up to 100 via two-descent.

Keyword(s).　 Elliptic curves having everywhere good reduction, Mordell-Weil groups, Two-descent