Three-Torsion Subgroups and Wild Conductors of Genus 3 Hyperelliptic Curves
arXiv:2210.02225 · doi:10.1016/j.jnt.2025.04.015
Abstract
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.
accepted version