## The arithmetic of elliptic curves—An update

- Benedict H. Gross, Gerd Faltings, Victor Kolyvagin, Richard Taylor
- 2006

- Published 2006

Given two elliptic curves defined over a number field K, not both with jinvariant zero, we show that there are infinitely many D ∈ K with pairwise distinct image in K/K 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.

@inproceedings{Wong200616J,
title={1 6 Ju n 20 06 QUADRATIC TWISTS OF PAIRS OF ELLIPTIC CURVES},
author={Siman Wong},
year={2006}
}