Elliptic curves with complex multiplication and abelian division fields

Asimina S. Hamakiotes, Alvaro Lozano-Robledo

Let $K$ be an imaginary quadratic field, and let ${\mathcal{O}}_{K,f}$ be an order in $K$ of conductor $f\ge 1$. Let $E$ be an elliptic curve with CM by ${\mathcal{O}}_{K,f}$, such th…