{"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/serre-curves-relative-to-obstructions-modulo","title":"Serre curves relative to obstructions modulo 2","arxiv_id":"2210.06645","date":"2022-10-13","proceeding":null,"authors":["Jacob Mayle","Rakvi"],"abstract":"We consider elliptic curves $E / \\mathbb{Q}$ for which the image of the adelic Galois representation $\\rho_E$ is as large as possible given a constraint on the image modulo 2. For such curves, we give a characterization in terms of their $\\ell$-adic images, compute all examples of conductor at most 500,000, precisely describe the image of $\\rho_E$, and offer an application to the cyclicity problem. In this way, we generalize some foundational results on Serre curves.","url_abs":"https://arxiv.org/abs/2210.06645v2","url_pdf":"https://arxiv.org/pdf/2210.06645v2.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":"serre-curves-relative-to-obstructions-modulo","repo_url":"https://github.com/maylejacobj/RelativeSerreCurves","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}