[{"extern":"1","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"02","scopus_import":"1","external_id":{"unknown":["1805.10709"]},"date_updated":"2025-07-10T11:51:49Z","citation":{"chicago":"Chan, Stephanie, Jeroen Hanselman, and Wanlin Li. “Ranks, 2-Selmer Groups, and Tamagawa Numbers of Elliptic Curves with ℤ∕2ℤ × ℤ∕8ℤ-Torsion.” <i>The Open Book Series</i>. Mathematical Sciences Publishers, 2019. <a href=\"https://doi.org/10.2140/obs.2019.2.173\">https://doi.org/10.2140/obs.2019.2.173</a>.","ieee":"S. Chan, J. Hanselman, and W. Li, “Ranks, 2-Selmer groups, and Tamagawa numbers of elliptic curves with ℤ∕2ℤ × ℤ∕8ℤ-torsion,” <i>The Open Book Series</i>, vol. 2. Mathematical Sciences Publishers, pp. 173–189, 2019.","ista":"Chan S, Hanselman J, Li W. 2019. Ranks, 2-Selmer groups, and Tamagawa numbers of elliptic curves with ℤ∕2ℤ × ℤ∕8ℤ-torsion. The Open Book Series. 2, 173–189.","mla":"Chan, Stephanie, et al. “Ranks, 2-Selmer Groups, and Tamagawa Numbers of Elliptic Curves with ℤ∕2ℤ × ℤ∕8ℤ-Torsion.” <i>The Open Book Series</i>, vol. 2, Mathematical Sciences Publishers, 2019, pp. 173–89, doi:<a href=\"https://doi.org/10.2140/obs.2019.2.173\">10.2140/obs.2019.2.173</a>.","ama":"Chan S, Hanselman J, Li W. Ranks, 2-Selmer groups, and Tamagawa numbers of elliptic curves with ℤ∕2ℤ × ℤ∕8ℤ-torsion. <i>The Open Book Series</i>. 2019;2:173-189. doi:<a href=\"https://doi.org/10.2140/obs.2019.2.173\">10.2140/obs.2019.2.173</a>","short":"S. Chan, J. Hanselman, W. Li, The Open Book Series 2 (2019) 173–189.","apa":"Chan, S., Hanselman, J., &#38; Li, W. (2019). Ranks, 2-Selmer groups, and Tamagawa numbers of elliptic curves with ℤ∕2ℤ × ℤ∕8ℤ-torsion. <i>The Open Book Series</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/obs.2019.2.173\">https://doi.org/10.2140/obs.2019.2.173</a>"},"type":"journal_article","year":"2019","publisher":"Mathematical Sciences Publishers","publication":"The Open Book Series","publication_identifier":{"issn":["2329-9061"],"eissn":["2329-907X"]},"author":[{"id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","first_name":"Yik Tung","orcid":"0000-0001-8467-4106","full_name":"Chan, Yik Tung","last_name":"Chan"},{"first_name":"Jeroen","full_name":"Hanselman, Jeroen","last_name":"Hanselman"},{"first_name":"Wanlin","full_name":"Li, Wanlin","last_name":"Li"}],"volume":2,"intvolume":"         2","date_published":"2019-02-13T00:00:00Z","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1805.10709","open_access":"1"}],"publication_status":"published","doi":"10.2140/obs.2019.2.173","_id":"19493","language":[{"iso":"eng"}],"day":"13","OA_place":"repository","oa_version":"Preprint","OA_type":"green","oa":1,"abstract":[{"text":"In 2016, Balakrishnan, Ho, Kaplan, Spicer, Stein and Weigandt produced a database of elliptic curves over Q ordered by height in which they computed the rank, the size of the 2-Selmer group, and other arithmetic invariants. They observed that after a certain point, the average rank seemed to decrease as the height increased. Here we consider the family of elliptic curves over \r\nQ whose rational torsion subgroup is isomorphic to Z∕2Z×Z∕8Z. Conditional on GRH and BSD, we compute the rank of 92% of the 202,461 curves with parameter height less than 103. We also compute the size of the 2-Selmer group and the Tamagawa product, and prove that their averages tend to infinity for this family.","lang":"eng"}],"title":"Ranks, 2-Selmer groups, and Tamagawa numbers of elliptic curves with ℤ∕2ℤ × ℤ∕8ℤ-torsion","date_created":"2025-04-05T10:51:07Z","status":"public","article_type":"original","article_processing_charge":"No","page":"173-189"}]