Existence of both principal and nonprincipal Steinitz classes for CM elliptic curves
Let K=Q(−D)K={\bf Q}(\sqrt{-D})K=Q(−D) with DDD prime and D≡1(mod4)D\equiv 1\pmod{4}D≡1(mod4), and let EEE be an elliptic curve having complex multiplication by OK{\cal O}_KOK. The Steinitz class St(E)St(E)St(E) is the…