{"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-primes-for-elliptic-curves-over","title":"Torsion primes for elliptic curves over degree 8 number fields","arxiv_id":"2304.14284","date":"2023-04-27","proceeding":null,"authors":["Maleeha Khawaja"],"abstract":"Let $d\\geq 1$ be an integer and let $p$ be a rational prime. Recall that $p$ is a torsion prime of degree $d$ if there exists an elliptic curve $E$ over a degree $d$ number field $K$ such that $E$ has a $K$-rational point of order $p$. Derickx, Kamienny, Stein and Stoll have computed the torsion primes of degrees 4, 5, 6 and 7; we verify that these techniques can be extended to determine the torsion primes of degree 8.","url_abs":"https://arxiv.org/abs/2304.14284v3","url_pdf":"https://arxiv.org/pdf/2304.14284v3.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-primes-for-elliptic-curves-over","repo_url":"https://github.com/maleehakhawaja/deg8torsionprimes","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}