Computing binary curves of genus five

2022/02/16 by Dušan Dragutinović, Dragutinović, Dušan · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Numerical Analysis Techniques #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.2202.07809

openalex publication_date 2022/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Genus 5 curves can be hyperelliptic, trigonal, or non-hyperelliptic non-trigonal, whose model is a complete intersection of three quadrics in ℙ⁴. We present and explain algorithms we used to determine, up to isomorphism over \mathbbF₂, all genus 5 curves defined over \mathbbF₂, and we do that separately for each of the three mentioned types. We consider these curves in terms of isogeny classes over \mathbbF₂ of their Jacobians or their Newton polygons, and for each of the three types, we compute the number of curves over \mathbbF₂ weighted by the size of their \mathbbF₂-automorphism groups.

Cited by

• On Weil Polynomials of Hyperelliptic Curves over Finite Fields of Characteristic 2
• An unusual family of supersingular curves of genus five

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