An atlas of the Richelot isogeny graph

4 Jan 2021 · Enric Florit, Benjamin Smith ·

We describe and illustrate the local neighbourhoods of vertices and edges in the (2, 2)-isogeny graph of principally polarized abelian surfaces, considering the action of automorphisms. Our diagrams are intended to build intuition for number theorists and cryptographers investigating isogeny graphs in dimension/genus 2, and the superspecial isogeny graph in particular.