Automorphisms and isogeny graphs of abelian varieties, with applications to the superspecial Richelot isogeny graph

no code implementations • 4 Jan 2021 • Enric Florit, Benjamin Smith

We investigate special structures due to automorphisms in isogeny graphs of principally polarized abelian varieties, and abelian surfaces in particular.

Cryptography and Security Number Theory

An atlas of the Richelot isogeny graph

no code implementations • 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.

Number Theory