Torsion points on y²=x⁶+1

1997/10/20 by José Felipe Voloch, Voloch, José Felipe
Mathematics · Social Sciences · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Communism, Protests, Social Movements #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/9710224

arxiv created 1997/10/20 · openalex publication_date 1997/10/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C be the curve y²=x⁶+1 of genus 2 over a field of characteristic zero. Consider C embedded in its Jacobian J by sending one of the points at infinity on C to the origin of J. In this brief note we show that the points of C whose image on J are torsion are precisely the two points at infinity and the six points with y=0.

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