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Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti, No. 519=18, 2014.

Original scientific paper

On quadratic twists of elliptic curves y2 = x(x − 1)(x − λ)

Andrej Dujella orcid id orcid.org/0000-0001-6867-5811 ; Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10000 Zagreb, Croatia
Ivica Gusić ; Faculty of Chemical Engin. and Techn., University of Zagreb, Marulićev trg 19, 10000 Zagreb, Croatia
Luka Lasić ; Faculty of Chemical Engin. and Techn., University of Zagreb, Marulićev trg 19, 10000 Zagreb, Croatia

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Abstract

Let E be an elliptic curve over Q given by y2 = f(x)
where f(x) = x(x − 1)(x − ). In this paper, we describe a construction
of twists E_g(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.

Keywords

Elliptic curve; quadratic twist

Hrčak ID:

127641

URI

https://hrcak.srce.hr/127641

Publication date:

30.9.2014.

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