{"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/explicit-isogenies-of-prime-degree-over","title":"Explicit isogenies of prime degree over quadratic fields","arxiv_id":"2101.02673","date":"2021-01-07","proceeding":null,"authors":["Barinder S. Banwait"],"abstract":"Let $K$ be a quadratic field which is not an imaginary quadratic field of class number one. We describe an algorithm to compute the primes $p$ for which there exists an elliptic curve over $K$ admitting a $K$-rational $p$-isogeny. This builds on work of David, Larson-Vaintrob, and Momose. Combining this algorithm with work of Bruin-Najman, \\\"{O}zman-Siksek, and most recently Box, we determine the above set of primes for the three quadratic fields $\\mathbb{Q}(\\sqrt{-10})$, $\\mathbb{Q}(\\sqrt{5})$, and $\\mathbb{Q}(\\sqrt{7})$, providing the first such examples after Mazur's 1978 determination for $K = \\mathbb{Q}$. The termination of the algorithm relies on the Generalised Riemann Hypothesis.","url_abs":"https://arxiv.org/abs/2101.02673v3","url_pdf":"https://arxiv.org/pdf/2101.02673v3.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":"explicit-isogenies-of-prime-degree-over","repo_url":"https://github.com/barinderbanwait/quadratic_isogeny_primes","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"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}