Improved bounds for Serre's open image theorem
Improved bounds for Serre's open image theorem
Let $E$ be an elliptic curve over the rationals which does not have complex multiplication. Serre showed that the adelic representation attached to $E/\mathbb{Q}$ has open image, and in particular there is a minimal natural number $C_E$ such that the mod $\ell$ representation $\bar{\rho}_{E,\ell}$ is surjective for any prime $\ell …