This paper is a contribution to the verification of conjectures of Birch and Swinnerton-Dyer about elliptic curves (1). The evidence that they produce is largely derived from curves with complex multiplication byi.In a previous paper (8), we had considered curves with complex multiplication by √ − 2. Here we shall look at the case when the ring of complex multiplications is isomorphic to the ring Z[ω], where ω3= 1, ω ≠ 1.