The Steinitz class of the Mordell-Weil group of some CM elliptic curves

Explicit complex multiplications for some elliptic curves with CM by O = Z[root-10] are given and used to determine the O-module structure of the Mordell-Weil groups of the curve over Q(root-10, root 5). The Steinitz class of these modules is determined and in particular shown not to be an isogeny invariant. (C) 1996 Academic Press, Inc.