Determination of elliptic curves with everywhere good reduction over real quadratic fields

Abstract

All elliptic curves having everywhere good reduction over \(\Bbb Q(\sqrt {29})\) are determined by studying the fields of 2- and 3-division points. As a byproduct of the argument, the elliptic curves over some real quadratic fields are determined. Though part of the result are already obtained in [2], [4], [5], [10], the proof given in the present paper is simpler.