Polarized products of elliptic curves with complex multiplication and field of moduli Q

Let be the maximal order in an imaginary quadratic field .We give an equivalence of categories between the category of polarized abelian varieties isomorphic to a product of elliptic curves over C with complex multiplication (CM) by and the category of integral hermitian -lattices.Then we apply this equivalence to enumerate all the genus 2 and 3 curves with field of moduli Q and with Jacobian isomorphic to a product of elliptic curves with CM by .