2017
DOI: 10.1016/j.jnt.2016.11.022
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High rank quadratic twists of pairs of elliptic curves

Abstract: Given a pair of elliptic curves E 1 and E 2 over the rational field Q whose jinvariants are not simultaneously 0 or 1728, Kuwata and Wang proved the existence of infinitely many square-free rationals d such that the d-quadratic twists of E 1 and E 2 are both of positive rank. We construct infinite families of pairs of elliptic curves E 1 and E 2 over Q such that for each pair there exist infinitely many square-free rationals d for which the d-quadratic twists of E 1 and E 2 are both of rank at least 2.

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