On possibilities of 3-adic Galois images associated to isogeny-torsion graphs

2023/07/09 by Rakvi
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2307.04074

openalex publication_date 2023/07/09 · openalex created_date 2023/07/12 · openalex updated_date 2026/07/28

Abstract

Let E be a non CM elliptic curve defined over \Q. There is an isogeny-torsion graph associated to E and there is also a Galois representation ρ_E,l^∞ \colon \Gal(\Qbar/\Q) → \GL₂(\ZZ_ℓ) associated to E for every prime ℓ. In this article, we explore the relation between these two objects when ℓ=3. More precisely, we give a classification of 3-adic Galois images associated to vertices of the isogeny-torsion graph of E.

Related

• 2-adic Galois images of non-CM isogeny-torsion graphs
• 2-adic images of CM isogeny-torsion graphs
• Infinite Families Of Isogeny-Torsion Graphs
• Wild Galois Representations: Elliptic curves over a 3-adic field
• Explicit open images for elliptic curves over ℚ