On products of quadratic twists and ranks of elliptic curves over large fields

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dc.contributor.authorIm, Bo-Haeko
dc.contributor.authorLozano-Robledo, Alvaroko
dc.date.accessioned2016-10-04T02:59:16Z-
dc.date.available2016-10-04T02:59:16Z-
dc.date.created2016-09-07-
dc.date.created2016-09-07-
dc.date.issued2009-02-
dc.identifier.citationJOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, v.79, pp.1 - 14-
dc.identifier.issn0024-6107-
dc.identifier.urihttp://hdl.handle.net/10203/213015-
dc.description.abstractIn this paper, we give examples of elliptic curves E/K over a number field K satisfying the property that there exist P(1), P(2) is an element of K[t] such that the twists E(P1), E(P2) and E(P1P2) are of positive rank over K(t). As a consequence of this result on twists, we show that for those elliptic curves E/K, and for each sigma is an element of Gal((K) over bar /K), the rank of E over the fixed field (K(ab))(sigma) under sigma is infinite, where K(ab) is the maximal abelian extension of K-
dc.languageEnglish-
dc.publisherOXFORD UNIV PRESS-
dc.subjectMORDELL-WEIL GROUPS-
dc.subjectPOINTS-
dc.titleOn products of quadratic twists and ranks of elliptic curves over large fields-
dc.typeArticle-
dc.identifier.wosid000264655100001-
dc.identifier.scopusid2-s2.0-58449133614-
dc.type.rimsART-
dc.citation.volume79-
dc.citation.beginningpage1-
dc.citation.endingpage14-
dc.citation.publicationnameJOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES-
dc.identifier.doi10.1112/jlms/jdn048-
dc.contributor.localauthorIm, Bo-Hae-
dc.contributor.nonIdAuthorLozano-Robledo, Alvaro-
dc.type.journalArticleArticle-
dc.subject.keywordPlusMORDELL-WEIL GROUPS-
dc.subject.keywordPlusPOINTS-
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