2-adic Galois images of non-CM isogeny-torsion graphs

2023/02/13 by Garen Chiloyan, Chiloyan, Garen · 1 citation
Mathematics · #11G05 #14H52 #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2302.06094

openalex publication_date 2023/02/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E be a ℚ-isogeny class of elliptic curves defined over ℚ without CM. The isogeny graph associated to E is a graph which has a vertex for each elliptic curve in E and an edge for each ℚ-isogeny of prime degree that maps one elliptic curve in E to another elliptic curve in E, with the degree recorded as a label of the edge. An isogeny-torsion graph is an isogeny graph where, in addition, we label each vertex with the abstract group structure of the torsion subgroup over ℚ of the corresponding elliptic curve. Then, the main statement of the article is a classification of the 2-adic image of Galois that occurs at each vertex of all isogeny-torsion graphs consisting of elliptic curves defined over ℚ without CM.

Cited by

• The possible adelic indices for elliptic curves admitting a rational cyclic isogeny

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