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DC Field | Value | Language |
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dc.citation.endPage | 132 | - |
dc.citation.number | 1 | - |
dc.citation.startPage | 123 | - |
dc.citation.title | JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY | - |
dc.citation.volume | 58 | - |
dc.contributor.author | Byeon, Dongho | - |
dc.contributor.author | Jeong, Keunyoung | - |
dc.contributor.author | Kim, Nayoung | - |
dc.date.accessioned | 2023-12-21T16:22:29Z | - |
dc.date.available | 2023-12-21T16:22:29Z | - |
dc.date.created | 2021-02-23 | - |
dc.date.issued | 2021-01 | - |
dc.description.abstract | Let K be a number field and L a finite abelian extension of K. Let E be an elliptic curve defined over K. The restriction of scalars Res(K)(L) E decomposes (up to isogeny) into abelian varieties over K Res(K)(L) E similar to circle plus(F is an element of S) A(F), where S is the set of cyclic extensions of K in L. It is known that if L is a quadratic extension, then A(L) is the quadratic twist of E. In this paper, we consider the case that K is a number field containing a primitive third root of unity, L = K((3)root D) is the cyclic cubic extension of K for some D is an element of K-x/(K-x)(3), E = E-a: y(2) = ( )x(3) + a is an elliptic curve with j-invariant 0 defined over K, and E-a(D) : y(2) = x(3) + aD(2) is the cubic twist of E-a. In this case, we prove A(L) is isogenous over K to E-a(D) x E-a(D2) and a property of the Selmer rank of A(L), which is a cubic analogue of a theorem of Mazur and Rubin on quadratic twists. |
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dc.identifier.bibliographicCitation | JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, v.58, no.1, pp.123 - 132 | - |
dc.identifier.doi | 10.4134/JKMS.j190867 | - |
dc.identifier.issn | 0304-9914 | - |
dc.identifier.scopusid | 2-s2.0-85099402601 | - |
dc.identifier.uri | https://scholarworks.unist.ac.kr/handle/201301/50038 | - |
dc.identifier.url | http://koreascience.or.kr/article/JAKO202109651118425.page | - |
dc.identifier.wosid | 000604421800007 | - |
dc.language | 영어 | - |
dc.publisher | KOREAN MATHEMATICAL SOC | - |
dc.title | RESTRICTION OF SCALARS AND CUBIC TWISTS OF ELLIPTIC CURVES | - |
dc.type | Article | - |
dc.description.isOpenAccess | FALSE | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied; Mathematics | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.type.docType | Article | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
dc.subject.keywordAuthor | Elliptic curve | - |
dc.subject.keywordAuthor | cubic twist | - |
dc.subject.keywordAuthor | restriction of scalars | - |
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