{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T08:32:12Z","timestamp":1776846732554,"version":"3.51.2"},"reference-count":18,"publisher":"American Mathematical Society (AMS)","issue":"276","license":[{"start":{"date-parts":[[2012,4,29]],"date-time":"2012-04-29T00:00:00Z","timestamp":1335657600000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We construct infinite families of elliptic curves with given torsion group structures over quartic number fields. In a 2006 paper, the first two authors and Park determined all of the group structures which occur infinitely often as the torsion of elliptic curves over quartic number fields. Our result presents explicit examples of their theoretical result. This paper also presents an efficient way of finding such families of elliptic curves with prescribed torsion group structures over quadratic or quartic number fields.<\/p>","DOI":"10.1090\/s0025-5718-2011-02493-2","type":"journal-article","created":{"date-parts":[[2011,4,29]],"date-time":"2011-04-29T13:34:24Z","timestamp":1304084064000},"page":"2395-2410","source":"Crossref","is-referenced-by-count":16,"title":["Families of elliptic curves over quartic number fields with prescribed torsion subgroups"],"prefix":"10.1090","volume":"80","author":[{"given":"Daeyeol","family":"Jeon","sequence":"first","affiliation":[]},{"given":"Chang Heon","family":"Kim","sequence":"additional","affiliation":[]},{"given":"Yoonjin","family":"Lee","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2011,4,29]]},"reference":[{"key":"1","series-title":"Graduate Texts in Mathematics","isbn-type":"print","volume-title":"Elliptic curves","volume":"111","author":"Husem\u00f6ller, Dale","year":"2004","ISBN":"https:\/\/id.crossref.org\/isbn\/0387954902","edition":"2"},{"issue":"273","key":"2","doi-asserted-by":"publisher","first-page":"579","DOI":"10.1090\/S0025-5718-10-02369-0","article-title":"Families of elliptic curves over cubic number fields with prescribed torsion subgroups","volume":"80","author":"Jeon, Daeyeol","year":"2011","journal-title":"Math. 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O\u2019Neil, Explicit descent over \ud835\udc4b(3) and \ud835\udc4b(5), arXiv:0201.5321 [math.NT] (2002)."},{"issue":"3","key":"11","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1142\/S0218196797000174","article-title":"Torsion groups of elliptic curves with integral \ud835\udc57-invariant over general cubic number fields","volume":"7","author":"Peth\u00f6, Attila","year":"1997","journal-title":"Internat. J. Algebra Comput.","ISSN":"https:\/\/id.crossref.org\/issn\/0218-1967","issn-type":"print"},{"issue":"3","key":"12","doi-asserted-by":"publisher","first-page":"831","DOI":"10.5802\/jtnb.428","article-title":"No 17-torsion on elliptic curves over cubic number fields","volume":"15","author":"Parent, Pierre","year":"2003","journal-title":"J. Th\\'{e}or. 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Sutherland, Constructing elliptic curves over finite fields with prescribed torsion, arXiv:0811.0296v2 [math.NT] (2008)."},{"key":"18","isbn-type":"print","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1090\/conm\/174\/01861","article-title":"Torsion groups of elliptic curves over cubic and certain biquadratic number fields","author":"Zimmer, Horst G.","year":"1994","ISBN":"https:\/\/id.crossref.org\/isbn\/0821851748"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/2011-80-276\/S0025-5718-2011-02493-2\/S0025-5718-2011-02493-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/2011-80-276\/S0025-5718-2011-02493-2\/S0025-5718-2011-02493-2.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T16:58:36Z","timestamp":1776790716000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/2011-80-276\/S0025-5718-2011-02493-2\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,4,29]]},"references-count":18,"journal-issue":{"issue":"276","published-print":{"date-parts":[[2011,10]]}},"alternative-id":["S0025-5718-2011-02493-2"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-2011-02493-2","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[2011,4,29]]}}}