Serre's Uniformity Conjecture for Elliptic Curves with Rational Cyclic Isogenies

Pedro Lemos

Let $E$ be an elliptic curve over $\mathbb{Q}$ such that ${\mathrm{End}}_{\bar{\mathbb{Q}}}(E)=\mathbb{Z}$ and which admits a non-trivial cyclic $\mathbb{Q}$-isogeny. We prove that,…