{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/three-torsion-subgroups-and-conductors-of","title":"Three-Torsion Subgroups and Conductors of Genus 3 Hyperelliptic Curves","arxiv_id":"2210.02225","date":"2022-10-05","proceeding":null,"authors":["Elvira Lupoian"],"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.","url_abs":"https://arxiv.org/abs/2210.02225v3","url_pdf":"https://arxiv.org/pdf/2210.02225v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"three-torsion-subgroups-and-conductors-of","repo_url":"https://github.com/elviralupoian/3torsionofgenus3hypcurves","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}