Gluing Genus 1 and Genus 2 Curves Along $\ell$-torsion

Pitchayut Saengrungkongka, Noah Walsh

Let $Y$ be a genus $2$ curve over $\mathbb{Q}$. We provide a method to systematically search for possible candidates of a prime $\ell \ge 3$ and a genus $1$ curve $X$ for which ther…