#### Positive rank quadratic twists of four elliptic curves

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dc.contributor.authorIm, Bo-Haeko
dc.date.accessioned2016-09-08T00:51:43Z-
dc.date.available2016-09-08T00:51:43Z-
dc.date.created2016-09-07-
dc.date.created2016-09-07-
dc.date.issued2013-02-
dc.identifier.citationJOURNAL OF NUMBER THEORY, v.133, no.2, pp.492 - 500-
dc.identifier.issn0022-314X-
dc.identifier.urihttp://hdl.handle.net/10203/212936-
dc.description.abstractLet K be a number field and E-i/K an elliptic curve defined over K for i = 1, 2, 3, 4. We prove that there exists a number field L containing K such that there are infinitely many d(k) is an element of L-x/(L-x)(2) such that E-i(dk)(L) has positive rank, equivalently all four elliptic curves E-i have growth of the rank over each of quadratic extensions L-k := L(root d(k)), more strongly, for any, i(1), i(2), ... , i(m). rank (E-i(l(i1) .. L-m)) &gt; rank(E-i(L-i1 ... Lim-1)) &gt; ... &gt;rank(E-i(L-i1)) &gt; rank(E-i(L)). We also prove that if each elliptic curve E-i for i = 1, 2,3 can be written in Legendre form over a cubic extension K of a number field k, then there are infinitely many d is an element of k(x)/(k(x))(2) such that E-i(d)(K) for i = 1, 2, 3 is of positive rank. (C) 2012 Elsevier Inc. All rights reserved-
dc.languageEnglish-
dc.subjectFIELDS-
dc.titlePositive rank quadratic twists of four elliptic curves-
dc.typeArticle-
dc.identifier.wosid000311769200010-
dc.identifier.scopusid2-s2.0-84867664964-
dc.type.rimsART-
dc.citation.volume133-
dc.citation.issue2-
dc.citation.beginningpage492-
dc.citation.endingpage500-
dc.citation.publicationnameJOURNAL OF NUMBER THEORY-
dc.identifier.doi10.1016/j.jnt.2012.08.023-
dc.contributor.localauthorIm, Bo-Hae-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorElliptic curve-