{"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/towards-a-classification-of-isolated-j","title":"Towards a classification of isolated $j$-invariants","arxiv_id":"2311.07740","date":"2023-11-13","proceeding":null,"authors":["Abbey Bourdon","Sachi Hashimoto","Timo Keller","Zev Klagsbrun","David Lowry-Duda","Travis Morrison","Filip Najman","Himanshu Shukla"],"abstract":"We develop an algorithm to test whether a non-CM elliptic curve $E/\\mathbb{Q}$ gives rise to an isolated point of any degree on any modular curve of the form $X_1(N)$. This builds on prior work of Zywina which gives a method for computing the image of the adelic Galois representation associated to $E$. Running this algorithm on all elliptic curves presently in the $L$-functions and Modular Forms Database and the Stein-Watkins Database gives strong evidence for the conjecture that $E$ gives rise to an isolated point on $X_1(N)$ if and only if $j(E)=-140625/8, -9317,$ $351/4$, or $-162677523113838677$.","url_abs":"https://arxiv.org/abs/2311.07740v4","url_pdf":"https://arxiv.org/pdf/2311.07740v4.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":"towards-a-classification-of-isolated-j","repo_url":"https://github.com/davidlowryduda/isolated_points","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null},{"paper_slug":"towards-a-classification-of-isolated-j","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}