{"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/distinct-differences-of-singular-moduli","title":"Distinct differences of singular moduli","arxiv_id":"2503.19686","date":"2025-03-25","proceeding":null,"authors":["Guy Fowler","Emanuele Tron"],"abstract":"Let $E_1, E_2 / \\mathbb{C}$ be non-isomorphic elliptic curves with complex multiplication. We prove that the pair $(E_1, E_2)$ is characterised, up to isomorphism, by the difference $j(E_1) - j(E_2)$ of the respective $j$-invariants. In other words, we show that if $x_1, x_2, x_3, x_4$ are singular moduli such that $x_1 - x_2 = x_3 - x_4$, then either $(x_1, x_2) = (x_3, x_4)$ or $(x_1, x_3) = (x_2, x_4)$.","url_abs":"https://arxiv.org/abs/2503.19686v1","url_pdf":"https://arxiv.org/pdf/2503.19686v1.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":"distinct-differences-of-singular-moduli","repo_url":"https://github.com/guyfowler/distinct_differences","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}