An unusual family of supersingular curves of genus five in characteristic two

Dušan Dragutinović

doi:10.1016/j.ffa.2025.102736

An unusual family of supersingular curves of genus five in characteristic two

Dušan Dragutinović

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

Abstract

We construct a family of smooth supersingular curves of genus 5 in characteristic 2 with several notable features: its dimension matches the expected dimension of any component of the supersingular locus in genus 5, its members are non-hyperelliptic curves with non-trivial automorphism groups, and each curve in the family admits a double cover structure over both an elliptic curve and a genus-2 curve. We also provide an explicit parametrization of this family.

Original language	English
Article number	102736
Number of pages	23
Journal	Finite Fields and Their Applications
Volume	110
DOIs	https://doi.org/10.1016/j.ffa.2025.102736
Publication status	Published - Feb 2026
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2025 The Author(s)

Keywords

Automorphisms
Characteristic 2
Curves
Finite fields
Jacobians
Supersingular

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10.1016/j.ffa.2025.102736Licence: CC BY

An unusual family of supersingular curves of genus five in characteristic twoFinal published version, 1.07 MBLicence: CC BY

Cite this

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abstract = "We construct a family of smooth supersingular curves of genus 5 in characteristic 2 with several notable features: its dimension matches the expected dimension of any component of the supersingular locus in genus 5, its members are non-hyperelliptic curves with non-trivial automorphism groups, and each curve in the family admits a double cover structure over both an elliptic curve and a genus-2 curve. We also provide an explicit parametrization of this family.",

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AB - We construct a family of smooth supersingular curves of genus 5 in characteristic 2 with several notable features: its dimension matches the expected dimension of any component of the supersingular locus in genus 5, its members are non-hyperelliptic curves with non-trivial automorphism groups, and each curve in the family admits a double cover structure over both an elliptic curve and a genus-2 curve. We also provide an explicit parametrization of this family.

KW - Automorphisms

KW - Characteristic 2

KW - Curves

KW - Finite fields

KW - Jacobians

KW - Supersingular

UR - https://www.scopus.com/pages/publications/105018068902

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DO - 10.1016/j.ffa.2025.102736

M3 - Article

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SN - 1071-5797

VL - 110

JO - Finite Fields and Their Applications

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M1 - 102736

ER -

An unusual family of supersingular curves of genus five in characteristic two

Abstract

Bibliographical note

Keywords

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