An unusual family of supersingular curves of genus five in characteristic two
Publication date
2026-02
Authors
Dragutinović, Dušan
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Document Type
Article
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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.
Keywords
Automorphisms, Characteristic 2, Curves, Finite fields, Jacobians, Supersingular, Theoretical Computer Science, Algebra and Number Theory, General Engineering, Applied Mathematics
Citation
Dragutinović, D 2026, 'An unusual family of supersingular curves of genus five in characteristic two', Finite Fields and Their Applications, vol. 110, 102736. https://doi.org/10.1016/j.ffa.2025.102736