{"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/intermediate-modular-curves-with-infinitely-1","title":"Intermediate modular curves with infinitely many quartic points","arxiv_id":"2504.15937","date":"2025-04-22","proceeding":null,"authors":["Maarten Derickx","Petar Orlić"],"abstract":"For every group $\\{\\pm1\\}\\subseteq \\Delta\\subseteq (\\mathbb Z/N\\mathbb Z)^\\times$, there exists an intermediate modular curve $X_\\Delta(N)$. In this paper we determine all curves $X_\\Delta(N)$ with infinitely many points of degree $4$ over $\\mathbb Q$. To do that, we developed a method to compute possible degrees of rational morphisms from $X_\\Delta(N)$ to an elliptic curve.","url_abs":"https://arxiv.org/abs/2504.15937v1","url_pdf":"https://arxiv.org/pdf/2504.15937v1.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":"intermediate-modular-curves-with-infinitely-1","repo_url":"https://github.com/nt-lib/quartic-xdelta","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}