The maximal abelian extension contained in a division field of an elliptic curve over Q with complex multiplication

Let K be an imaginary quadratic field, and let OK,f be an order in K of conductor f≥ 1. Let E be an elliptic curve with CM by OK,f, such that E is defined by a model over Q(jK,f), where jK,f=j(E). It has been shown by the author and Lozano-Robledo that Gal(Q(jK,f,E[N])/Q(jK,f)) is only abelian for $N=2,3$, and $4$. Let p be a prime and let n≥ 1 be an integer. In this article, we bound the commutator subgroups of Gal(Q(E[pⁿ])/Q) and classify the maximal abelian extensions contained in Q(E[pⁿ])/Q.