Coincidences of division fields

Harris B. Daniels, Álvaro Lozano-Robledo

Let $E$ be an elliptic curve defined over $\mathbb{Q}$, and let ${\rho }_E:\mathrm{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})\to \mathrm{GL}(2,\hat{\mathbb{Z}})$ be the adelic represen…