Ordinary isogeny graphs with level structure

2025/03/27 by Derek Perrin, José Felipe Voloch · 1 voice
Computer Science · Mathematics · #Advanced Graph Theory Research #Graph Labeling and Dimension Problems #Graph theory and applications

paper · pdf · doi:10.4153/s0008439525000372

openalex publication_date 2025/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/26

Abstract

Abstract We study ℓ -isogeny graphs of ordinary elliptic curves defined over \mathbb F_q with an added level structure. Given an integer N coprime to p and ℓ , we look at the graphs obtained by adding Γ ₀(N) , Γ ₁(N), and Γ (N) -level structures to volcanoes. Given an order \mathcal O in an imaginary quadratic field K, we look at the action of generalized ideal class groups of \mathcal O on the set of elliptic curves whose endomorphism rings are \mathcal O along with a given level structure. We show how the structure of the craters of these graphs is determined by the choice of parameters.

Discussions

• I'm excited to share that my first research paper, "Ordinary isogeny graphs with level structure," has been published in the Canadian Mathematical Bulletin! This marks a huge milestone in my research [bsky, 1 points, 1 comments]

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