Rational points on $X_0(N{)}^{\ast }$ when $N$ is non-squarefree

Sachi Hashimoto, Timo Keller, Samuel Le Fourn

Let $N$ be a non-squarefree integer such that the quotient $X_0(N{)}^{\ast }$ of the modular curve $X_0(N)$ by the full group of Atkin-Lehner involutions has positive genus. Elkies conject…