{"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/formalized-class-group-computations-and","title":"Formalized Class Group Computations and Integral Points on Mordell Elliptic Curves","arxiv_id":"2209.15492","date":"2022-09-30","proceeding":null,"authors":["Anne Baanen","Alex J. Best","Nirvana Coppola","Sander R. Dahmen"],"abstract":"Diophantine equations are a popular and active area of research in number theory. In this paper we consider Mordell equations, which are of the form $y^2=x^3+d$, where $d$ is a (given) nonzero integer number and all solutions in integers $x$ and $y$ have to be determined. One non-elementary approach for this problem is the resolution via descent and class groups. Along these lines we formalized in Lean 3 the resolution of Mordell equations for several instances of $d<0$. In order to achieve this, we needed to formalize several other theories from number theory that are interesting on their own as well, such as ideal norms, quadratic fields and rings, and explicit computations of the class number. Moreover we introduced new computational tactics in order to carry out efficiently computations in quadratic rings and beyond.","url_abs":"https://arxiv.org/abs/2209.15492v2","url_pdf":"https://arxiv.org/pdf/2209.15492v2.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":"formalized-class-group-computations-and","repo_url":"https://github.com/lean-forward/class-group-and-mordell-equation","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}