Bounds on Heights of $2$-isogeny Graphs in Ordinary Curves over ${\mathbb{F}}_p$ and ${\mathbb{F}}_{p^2}$ and Its Application

Yuji Hashimoto, Koji Nuida

It is known that any isogeny graph consisting of ordinary elliptic curves over ${\mathbb{F}}_q$ with $q=p$ or $p^2$ has a special structure, called a volcano graph. We have a bound…