Let C be an elliptic curve over an affine scheme S, and let E be an even periodic ring spectrum whose associated formal group is the formal completion of C. This makes E an elliptic spectrum''. Now let A be a finite abelian group. We will describe what it means for an A-equivariant ring spectrum EA to be an equivariant version'' of E, in terms of the theory of equivariant formal groups. We will show how to construct EA when E is K(n)-local for some n. We will then give a method for recovering the general case from the K(n)-local case. The method always produces an A-spectrum EA, but it may not be well-defined or have a ring structure. We will describe some cases in which one can get around these problems.