engleski

On quadratic twists of elliptic curves y^2=x(x-1)(x-lambda)

Let E be an elliptic curve over Q given by y^2 = f(x) where f(x) = x(x − 1)(x − lambda). 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.

Elliptic curve ; quadratic twist

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