Elliptic curves with all cubic twists of the same root number.

Abstract: Let be an elliptic curve with j-invariant 0 defined over a number field K. In this paper, we give a simple condition on K which determines whether all cubic twists of have the same root number or not. This is a cubic twist analogue to the work [D-D] of Dokchitser and Dokchitser on quadratic twists of elliptic curves. [Copyright &y& Elsevier]