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

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In 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
Publisher
OXFORD UNIV PRESS
Issue Date
2009-02
Language
English
Article Type
Article
Keywords

MORDELL-WEIL GROUPS; POINTS

Citation

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, v.79, pp.1 - 14

ISSN
0024-6107
DOI
10.1112/jlms/jdn048
URI
http://hdl.handle.net/10203/213015
Appears in Collection
MA-Journal Papers(저널논문)
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