Hyperelliptic curves covering an elliptic curve twice

2013/03/18 by Xavier Xarles, Xarles, Xavier
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1303.4220

openalex publication_date 2013/03/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that for any elliptic curve (with j invariant not 0 or 1728) over any field of characteristic different from 2 and 3, there exists an hyperelliptic curve H of genus 5 with two independent maps to the given elliptic curve. We also show that, if we want such a curve to be just geometrically hyperelliptic, so having a degree two map to a conic, then there are some with genus 3.

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