{"type":"journal_article","status":"public","publication_identifier":{"issn":["2329-9061"],"eissn":["2329-907X"]},"month":"02","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","year":"2019","publication":"The Open Book Series","page":"173-189","oa_version":"Preprint","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","external_id":{"unknown":["1805.10709"]},"extern":"1","date_published":"2019-02-13T00:00:00Z","date_created":"2025-04-05T10:51:07Z","quality_controlled":"1","volume":2,"date_updated":"2025-04-08T11:01:10Z","intvolume":"         2","language":[{"iso":"eng"}],"article_type":"original","publisher":"Mathematical Sciences Publishers","OA_type":"green","publication_status":"published","article_processing_charge":"No","day":"13","scopus_import":"1","author":[{"first_name":"Yik Tung","orcid":"0000-0001-8467-4106","full_name":"Chan, Yik Tung","id":"c4c0afc8-9262-11ed-9231-d8b0bc743af1","last_name":"Chan"},{"full_name":"Hanselman, Jeroen","first_name":"Jeroen","last_name":"Hanselman"},{"last_name":"Li","first_name":"Wanlin","full_name":"Li, Wanlin"}],"_id":"19493","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1805.10709"}],"OA_place":"repository","doi":"10.2140/obs.2019.2.173","oa":1}