### Steinitz Class of Mordell Groups of Elliptic Curves With Complex Multiplication, by Tong Liu and Xianke Zhang

Let E be an elliptic curve having Complex Multiplication by the full
ring O_K of integers of K=Q(\sqrt{-D}), let H=K(j(E)) be the Hilbert
class field of K. Then the Mordell-Weil group E(H) is an O_K-module,
and its structure denpends on its Steinitz class St(E), which is studied
here. In partucular, when D is a prime number, it is proved that
St(E)=1
if D\equiv 3 (mod 4); and St(E)=[P]^t if D\equiv 1 (mod 4), where [P]
is the ideal class of K represented by prime factor P of 2 in K, t is a
fixed integer. General structures are also discussed for St(E) and for
modules over Dedekind domain. These results develop the results by D.
Dummit and W. Miller for D=10 and some elliptic curves to more general D
and general elliptic curves.

Tong Liu and Xianke Zhang <xianke@tsinghua.edu.cn>