Quadratic twists of pairs of elliptic curves
Abstract
Given two elliptic curves defined over a number field K, not both with jinvariant 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 MordellWeil 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606405
 Bibcode:
 2006math......6405W
 Keywords:

 Mathematics  Number Theory;
 11G05