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

Sachi Hashimoto, Timo Keller, Samuel Le Fourn

Let $N$ be a positive integer and $X_0(N{)}^{\ast }$ be the quotient of the modular curve $X_0(N)$ by its full group of Atkin-Lehner involutions. Elkies conjectures that the rational point…