Degrees of abelian subvarieties of powers of elliptic curves over the complex numbers

We determine the degrees of abelian subvarieties of a power of an elliptic curve E over $\doubc$, where the degree is with respect to the embedding obtained via the linear space associated to a theta-function on the subspace underlying the subvariety whose associated forms are equal to the restriction of the forms associated to a theta-function for the power of E. We express the degree of an abelian subvariety Y in terms of a system of linear equations with coefficients in the endomorphism ring of E which the subspace underlying Y satisfies. We reformulate this expression of the degree in terms of the height of an algebraic subspace of K$\sp{n}$, where K is the field of fractions of the endomorphism ring of E.