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