{"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/computing-p-adic-heights-on-hyperelliptic","title":"Computing p-adic heights on hyperelliptic curves","arxiv_id":"2307.15787","date":"2023-07-28","proceeding":null,"authors":["Stevan Gajović","J. Steffen Müller"],"abstract":"We describe an algorithm to compute the local Coleman-Gross p-adic height at p on a hyperelliptic curve. Previously, this was only possible using an algorithm due to Balakrishnan and Besser, which was limited to odd degree. While we follow their general strategy, our algorithm is significantly faster and simpler and works for both odd and even degree. We discuss a precision analysis and an implementation in SageMath. Our work has several applications, also discussed in this article. These include various versions of the quadratic Chabauty method, and numerical evidence for a p-adic version of the conjecture of Birch and Swinnerton-Dyer in cases where this was not previously possible.","url_abs":"https://arxiv.org/abs/2307.15787v4","url_pdf":"https://arxiv.org/pdf/2307.15787v4.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":"computing-p-adic-heights-on-hyperelliptic","repo_url":"https://github.com/steffenmueller/QCMod","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}