An atlas of the Richelot isogeny graph

Enric Florit (1) , Benjamin Smith (2)

1 UB - Universitat de Barcelona
2 GRACE - Geometry, arithmetic, algorithms, codes and encryption

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.

Domaines: Théorie des nombres [math.NT]

Enric Florit, Benjamin Smith. An atlas of the Richelot isogeny graph. RIMS Kôkyûroku Bessatsu, 2022, Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties, B90, pp.195-219. ⟨hal-03094296v2⟩