{"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/elliptic-curves-over-mathbb-q-and-2-adic","title":"Elliptic curves over $\\mathbb{Q}$ and 2-adic images of Galois","arxiv_id":"1402.5997","date":"2014-02-24","proceeding":null,"authors":["Jeremy Rouse","David Zureick-Brown"],"abstract":"We give a classification of all possible $2$-adic images of Galois representations associated to elliptic curves over $\\mathbb{Q}$. To this end, we compute the 'arithmetically maximal' tower of 2-power level modular curves, develop techniques to compute their equations, and classify the rational points on these curves.","url_abs":"http://arxiv.org/abs/1402.5997v3","url_pdf":"http://arxiv.org/pdf/1402.5997v3.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":"elliptic-curves-over-mathbb-q-and-2-adic","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}