gross has refined the birch--swinnerton-dyer conjecture in the case of an elliptic curve with complex multiplication by a nonmaximal order. gross' conjecture has been reformulated in the language of derived categories and determinants of perfect complexes. burns and flach have realized that this immediately leads to a refinement of gross' conjecture. the conjecture is now expressed as a statement concerning a generator of the image of a map of 1-dimensional modules. this conjecture is proved by a construction which shows it to follow from the explicit reciprocity law and rubin's main conjecture.