{"year":"2024","status":"public","arxiv":1,"abstract":[{"lang":"eng","text":"Consider the family of elliptic curves En:y2=x3+n2, where n varies over positive cubefree integers. There is a rational 3-isogeny ϕ from En to E^n:y2=x3−27n2 and a dual isogeny ϕ^:E^n→En. We show that for almost all n, the rank of Selϕ(En) is 0, and the rank of Selϕ^(E^n) is determined by the number of prime factors of n that are congruent to 2mod3 and the congruence class of nmod9."}],"date_created":"2025-04-05T10:50:33Z","type":"journal_article","issue":"9","volume":2024,"publisher":"Oxford University Press","citation":{"apa":"Chan, S. (2024). The 3-isogeny selmer groups of the elliptic curves y2=x3+n2. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href=\"https://doi.org/10.1093/imrn/rnad266\">https://doi.org/10.1093/imrn/rnad266</a>","ama":"Chan S. The 3-isogeny selmer groups of the elliptic curves y2=x3+n2. <i>International Mathematics Research Notices</i>. 2024;2024(9):7571-7593. doi:<a href=\"https://doi.org/10.1093/imrn/rnad266\">10.1093/imrn/rnad266</a>","short":"S. Chan, International Mathematics Research Notices 2024 (2024) 7571–7593.","mla":"Chan, Stephanie. “The 3-Isogeny Selmer Groups of the Elliptic Curves Y2=x3+n2.” <i>International Mathematics Research Notices</i>, vol. 2024, no. 9, Oxford University Press, 2024, pp. 7571–93, doi:<a href=\"https://doi.org/10.1093/imrn/rnad266\">10.1093/imrn/rnad266</a>.","chicago":"Chan, Stephanie. “The 3-Isogeny Selmer Groups of the Elliptic Curves Y2=x3+n2.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2024. <a href=\"https://doi.org/10.1093/imrn/rnad266\">https://doi.org/10.1093/imrn/rnad266</a>.","ista":"Chan S. 2024. The 3-isogeny selmer groups of the elliptic curves y2=x3+n2. International Mathematics Research Notices. 2024(9), 7571–7593.","ieee":"S. Chan, “The 3-isogeny selmer groups of the elliptic curves y2=x3+n2,” <i>International Mathematics Research Notices</i>, vol. 2024, no. 9. Oxford University Press, pp. 7571–7593, 2024."},"article_processing_charge":"No","acknowledgement":"The author would like to thank Peter Koymans and Carlo Pagano for helpful discussions.","OA_type":"green","scopus_import":"1","extern":"1","title":"The 3-isogeny selmer groups of the elliptic curves y2=x3+n2","external_id":{"arxiv":["2211.06062"]},"month":"05","date_published":"2024-05-01T00:00:00Z","intvolume":"      2024","author":[{"last_name":"Chan","first_name":"Yik Tung","orcid":"0000-0001-8467-4106","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","full_name":"Chan, Yik Tung"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","quality_controlled":"1","OA_place":"repository","language":[{"iso":"eng"}],"day":"01","publication_identifier":{"issn":["1073-7928"],"eissn":["1687-0247"]},"article_type":"original","page":"7571-7593","date_updated":"2025-07-10T11:51:44Z","doi":"10.1093/imrn/rnad266","publication":"International Mathematics Research Notices","oa_version":"Preprint","publication_status":"published","_id":"19486","oa":1,"main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2211.06062","open_access":"1"}]}