## JMI2011B-4 Non-existence of elliptic curves with everywhere good reduction over some real quadratic fields (pp.113-117)

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

J. Math-for-Ind. 3B (2011) 113-117.

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