Let K be an imaginary quadratic field, and let O_{K,f} be an order in K of conductor f at least 1. Let E be an elliptic curve with complex multiplication by O_{K,f}, such that E is defined by a model over Q(j(E)), where j(E) is the j-invariant of E. Let N\geq 2 be an integer. The extension Q(j(E), E[N])/Q}(j(E)) is usually not abelian; it is only abelian for N=2,3, and 4. Let p be a prime and let n at least 1 be an integer. In this talk, we will classify the maximal abelian extension contained in Q(E[p^n])/Q.