# Geometry and Arithmetic

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#### DOI: 10.4171/119-1/19

On the modular curve X0(23)

René Schoof[1]

(1) Università di Roma Tor Vergata, Italy

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 $J_0(23)$.

Keywords: Group schemes, modular curves, algebraic number fields