{"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/on-the-torsion-of-rational-elliptic-curves-1","title":"On the torsion of rational elliptic curves over sextic fields","arxiv_id":"1808.02887","date":"2018-08-08","proceeding":null,"authors":["Harris B. Daniels","Enrique González-Jiménez"],"abstract":"Given an elliptic curve $E/\\mathbb{Q}$ with torsion subgroup $G = E(\\mathbb{Q})_{\\rm tors}$ we study what groups (up to isomorphism) can occur as the torsion subgroup of $E$ base-extended to $K$, a degree 6 extension of $\\mathbb{Q}$. We also determine which groups $H = E(K)_{\\rm tors}$ can occur infinitely often and which ones occur for only finitely many curves. This article is a first step towards a complete classification of torsion growth of over sextic fields.","url_abs":"https://arxiv.org/abs/1808.02887v2","url_pdf":"https://arxiv.org/pdf/1808.02887v2.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":"on-the-torsion-of-rational-elliptic-curves-1","repo_url":"https://github.com/abbey-bourdon/rational-isolated-prime-power","is_official":0,"mentioned_in_paper":0,"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}