{"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/torsion-subgroups-of-elliptic-curves-over","title":"Torsion subgroups of elliptic curves over quintic and sextic number fields","arxiv_id":"1608.07549","date":"2016-08-26","proceeding":null,"authors":["Maarten Derickx","Andrew V. Sutherland"],"abstract":"Let $\\Phi^\\infty(d)$ denote the set of finite abelian groups that occur infinitely often as the torsion subgroup of an elliptic curve over a number field of degree $d$. The sets $\\Phi^\\infty(d)$ are known for $d\\le 4$. In this article we determine $\\Phi^\\infty(5)$ and $\\Phi^\\infty(6)$.","url_abs":"http://arxiv.org/abs/1608.07549v3","url_pdf":"http://arxiv.org/pdf/1608.07549v3.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":"torsion-subgroups-of-elliptic-curves-over","repo_url":"https://github.com/koffie/mdmagma","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}