Local-global principle for 11-isogenies of elliptic curves is true over quadratic fields

2025/01/29 by Stevan Gajović, Gajović, Stevan, Jeroen Hanselman +3
Mathematics · #11G18 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Number Theory (math.NT) #Primary 14G05 #Secondary 11G05 #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2501.17602

openalex publication_date 2025/01/29 · openalex created_date 2025/01/31 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that the local-global principle of 11-isogenies for elliptic curves over quadratic fields does not fail. This gives a positive answer to a conjecture by Banwait and Cremona. The proof is based on the determination of the set of quadratic points on the modular curve X_D₁₀(11).

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