Mathematics > Number Theory
[Submitted on 5 Oct 2022 (v1), last revised 15 Aug 2023 (this version, v3)]
Title:Three-Torsion Subgroups and Conductors of Genus 3 Hyperelliptic Curves
View PDFAbstract:We give a practical method for computing the 3-torsion subgroup of the Jacobian of a genus 3 hyperelliptic curve. We define a scheme for the 3-torsion points of the Jacobian and use complex approximations, homotopy continuation and lattice reduction to find precise expression for the 3-torsion. In the latter stages of the paper, we explain how the 3-torsion subgroup can be used to compute the wild part of the local exponent of the conductor at 2.
Submission history
From: Elvira Lupoian [view email][v1] Wed, 5 Oct 2022 13:03:54 UTC (18 KB)
[v2] Sat, 8 Oct 2022 21:20:21 UTC (18 KB)
[v3] Tue, 15 Aug 2023 13:02:55 UTC (20 KB)
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