%0 Journal Article
%T Quadratic twists of pairs of elliptic curves
%A Siman Wong
%J Mathematics
%D 2006
%I arXiv
%X Given two elliptic curves defined over a number field K, not both with j-invariant zero, we show that there are infinitely many $D\in K^\times$ with pairwise distinct image in $ K^\times/{K^\times}^2 $, such that the quadratic twist of both curves by D have positive Mordell-Weil rank. The proof depends on relating the values of pairs of cubic polynomials to rational points on another elliptic curve, and on a fiber product construction.
%U http://arxiv.org/abs/math/0606405v1