Rad HAZU, Matematičke znanosti, Vol. 18 (2014), 27-34.

ON QUADRATIC TWISTS OF ELLIPTIC CURVES y2 = x(x - 1)(x - λ)

Andrej Dujella, Ivica Gusić and Luka Lasić

Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
e-mail: duje@math.hr

Faculty of Chemical Engin. and Techn., University of Zagreb, Marulićev trg 19, 10000 Zagreb, Croatia
e-mail: igusic@fkit.hr

Faculty of Chemical Engin. and Techn., University of Zagreb, Marulićev trg 19, 10000 Zagreb, Croatia
e-mail: llasic@fkit.hr

Abstract.   Let E be an elliptic curve over Q given by y2 = f(x) where f(x) = x(x - 1)(x - λ). In this paper, we describe a construction of twists Eg(u) of rank 2 over Q(u), where g(u) are polynomials over Q. The construction leads to two sets of twists: the first consists of five twists obtained by Rubin and Silverberg with a different method, while the second consists of five new twists.

2010 Mathematics Subject Classification.   11G05, 14H52.

Key words and phrases.   Elliptic curve, quadratic twist.

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References:

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