{"language":[{"iso":"eng"}],"type":"journal_article","intvolume":"       388","publisher":"Springer Nature","external_id":{"arxiv":["2203.11366"]},"doi":"10.1007/s00208-023-02578-x","publication_status":"published","_id":"19487","day":"07","quality_controlled":"1","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.2203.11366","open_access":"1"}],"arxiv":1,"author":[{"orcid":"0000-0001-8467-4106","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","first_name":"Yik Tung","last_name":"Chan","full_name":"Chan, Yik Tung"}],"status":"public","year":"2023","date_created":"2025-04-05T10:50:37Z","page":"2275-2288","article_processing_charge":"No","extern":"1","month":"02","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa":1,"citation":{"chicago":"Chan, Stephanie. “Integral Points on Cubic Twists of Mordell Curves.” <i>Mathematische Annalen</i>. Springer Nature, 2023. <a href=\"https://doi.org/10.1007/s00208-023-02578-x\">https://doi.org/10.1007/s00208-023-02578-x</a>.","mla":"Chan, Stephanie. “Integral Points on Cubic Twists of Mordell Curves.” <i>Mathematische Annalen</i>, vol. 388, no. 3, Springer Nature, 2023, pp. 2275–88, doi:<a href=\"https://doi.org/10.1007/s00208-023-02578-x\">10.1007/s00208-023-02578-x</a>.","ista":"Chan S. 2023. Integral points on cubic twists of Mordell curves. Mathematische Annalen. 388(3), 2275–2288.","ama":"Chan S. Integral points on cubic twists of Mordell curves. <i>Mathematische Annalen</i>. 2023;388(3):2275-2288. doi:<a href=\"https://doi.org/10.1007/s00208-023-02578-x\">10.1007/s00208-023-02578-x</a>","short":"S. Chan, Mathematische Annalen 388 (2023) 2275–2288.","ieee":"S. Chan, “Integral points on cubic twists of Mordell curves,” <i>Mathematische Annalen</i>, vol. 388, no. 3. Springer Nature, pp. 2275–2288, 2023.","apa":"Chan, S. (2023). Integral points on cubic twists of Mordell curves. <i>Mathematische Annalen</i>. Springer Nature. <a href=\"https://doi.org/10.1007/s00208-023-02578-x\">https://doi.org/10.1007/s00208-023-02578-x</a>"},"abstract":[{"text":"Fix a non-square integer 𝑘≠0. We show that the number of curves 𝐸𝐵:𝑦^2=𝑥^3+𝑘𝐵^2 containing an integral point, where B ranges over positive integers less than N, is bounded by ≪𝑘𝑁(log𝑁)−1/2+𝜖. In particular, this implies that the number of positive integers 𝐵≤𝑁 such that −3𝑘𝐵^2 is the discriminant of an elliptic curve over 𝑄 is o(N). The proof involves a discriminant-lowering procedure on integral binary cubic forms.","lang":"eng"}],"title":"Integral points on cubic twists of Mordell curves","date_updated":"2025-07-10T11:51:45Z","publication":"Mathematische Annalen","date_published":"2023-02-07T00:00:00Z","OA_type":"green","publication_identifier":{"issn":["0025-5831"],"eissn":["1432-1807"]},"article_type":"original","oa_version":"Preprint","OA_place":"repository","issue":"3","scopus_import":"1","volume":388}