Computing binary curves of genus five

Dušan Dragutinović

doi:10.1016/j.jpaa.2023.107522

Computing binary curves of genus five

Research output: Contribution to journal › Article › Academic › peer-review

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 F₂, all genus 5 curves defined over F₂, and we do that separately for each of the three mentioned types. We consider these curves in terms of isogeny classes over F₂ of their Jacobians or their Newton polygons, and for each of the three types, we compute the number of curves over F₂ weighted by the size of their F₂-automorphism groups.

Original language	English
Article number	107522
Journal	Journal of Pure and Applied Algebra
Volume	228
Issue number	4
DOIs	https://doi.org/10.1016/j.jpaa.2023.107522
Publication status	Published - Apr 2024

Keywords

Curves
Finite fields
Genus five

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10.1016/j.jpaa.2023.107522Licence: CC BY

1-s2.0-S0022404923002049-mainFinal published version, 422 KBLicence: CC BY

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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 F2, all genus 5 curves defined over F2, and we do that separately for each of the three mentioned types. We consider these curves in terms of isogeny classes over F2 of their Jacobians or their Newton polygons, and for each of the three types, we compute the number of curves over F2 weighted by the size of their F2-automorphism groups.",

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AB - 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 F2, all genus 5 curves defined over F2, and we do that separately for each of the three mentioned types. We consider these curves in terms of isogeny classes over F2 of their Jacobians or their Newton polygons, and for each of the three types, we compute the number of curves over F2 weighted by the size of their F2-automorphism groups.

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KW - Finite fields

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Computing binary curves of genus five

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Keywords

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