An atlas of the Richelot isogeny graph

2021/01/04 by Enric Florit, Benjamin Smith, Florit, Enric +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Graph Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT) #graph theory and CDMA systems #math.NT

paper · pdf · doi:10.48550/arxiv.2101.00917

openalex publication_date 2021/01/04 · arxiv created 2021/01/05 · arxiv updated 2021/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• Exact Stratification and Affine Mass Formulas for Split Richelot Data over Finite Fields

Related

• Counting Richelot isogenies between superspecial abelian surfaces
• Isogeny graphs of superspecial abelian varieties
• Isogeny graphs of ordinary abelian varieties
• Neighborhood of vertices in the isogeny graph of principally polarized superspecial abelian surfaces
• Isogeny graphs with maximal real multiplication