# On the modular curve <em>X</em><sub>0</sub>(23)

• ### René Schoof

Università di Roma Tor Vergata, Italy

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## 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 $J_0(23)$.