Quadratic twists of pairs of elliptic curves

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dc.creatorWong, Siman
dc.date2006-06-16
dc.date.accessioned2026-07-07T07:17:22Z
dc.date.available2026-07-07T07:17:22Z
dc.descriptionGiven 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.
dc.identifierhttps://arxiv.org/abs/math/0606405
dc.identifierhttp://arxiv.org/abs/math/0606405
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/113916
dc.subjectNumber Theory
dc.subject11G05
dc.titleQuadratic twists of pairs of elliptic curves
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