On products of quadratic twists and ranks of elliptic curves over large fields
- Authors
- Im, Bo-Hae; Lozano-Robledo, Alvaro
- Issue Date
- Feb-2009
- Publisher
- WILEY
- Citation
- JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, v.79, no.1, pp 1 - 14
- Pages
- 14
- Journal Title
- JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
- Volume
- 79
- Number
- 1
- Start Page
- 1
- End Page
- 14
- URI
- https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/65293
- DOI
- 10.1112/jlms/jdn048
- ISSN
- 0024-6107
1469-7750
- Abstract
- 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.
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Collections - College of Natural Sciences > Department of Mathematics > 1. Journal Articles
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