A note on 8-division fields of elliptic curves

2017/04/20 by Jeffrey Yelton, Yelton, Jeffrey
Mathematics · #11G05 #12F10 #14G32 #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1704.06190

openalex publication_date 2017/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a field of characteristic different from 2 and let E be an elliptic curve over K, defined either by an equation of the form y² = f(x) with degree 3 or as the Jacobian of a curve defined by an equation of the form y² = f(x) with degree 4. We obtain generators over K of the 8-division field K(E[8]) of E given as formulas in terms of the roots of the polynomial f, and we explicitly describe the action of a particular automorphism in Gal(K(E[8]) / K).

Citations

• Good Reduction of Abelian Varieties

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