{"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/models-of-cm-elliptic-curves-with-a","title":"Models of CM elliptic curves with a prescribed $\\ell$-adic Galois image","arxiv_id":"2408.04159","date":"2024-08-08","proceeding":null,"authors":["Enrique González-Jiménez","Álvaro Lozano-Robledo","Benjamin York"],"abstract":"For each prime number $\\ell$ and for each imaginary quadratic order of class number one or two, we determine all the possible $\\ell$-adic Galois representations that occur for any elliptic curve with complex multiplication by such an order over its minimal field of definition, and then we determine all the isomorphism classes of elliptic curves that have a prescribed $\\ell$-adic Galois representation.","url_abs":"https://arxiv.org/abs/2408.04159v3","url_pdf":"https://arxiv.org/pdf/2408.04159v3.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":"models-of-cm-elliptic-curves-with-a","repo_url":"https://github.com/benjamin-york/cm-galois-images","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}