On the modular curve $X_0(23)$

Abstract

The Jacobian $J_0(23)$ of the modular curve $X_0(23)$ is a semi-stable abelian variety over $\mathbb{Q}$ with good reduction outside 23. It is simple. We prove that every simple semi-stable abelian variety over $\mathbb{Q}$ with good reduction outside 23 is isogenous over $\mathbb{Q}$ to $J_0(23)$.