Number Theory
On the proportion of rank 0 twists of elliptic curves
Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 483-486.

Let E be an elliptic curve defined over Q, let Ed denote its dth quadratic twist, and rEd:=rankEd(Q). We prove, that, for any positive integer k there are pairwise non-isogenous elliptic curves E1,,Ek such that rE1p==rEkp=0 for a positive proportion of primes p.

Soit E une courbe elliptique définie sur Q, Ed la tordue quadratique de E par d, et rEd:=rangEd(Q). On démontre qu'il existe, pour tout entier positif k, des courbes elliptiques E1,,Ek, qui sont 2 à 2 non isogènes, et telles que rE1p==rEkp=0 pour une famille de nombres premiers p de densité positive.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.03.025
Dąbrowski, Andrzej 1

1 Institute of Mathematics, University of Szczecin, ul. Wielkopolska 15, 70-451 Szczecin, Poland
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Dąbrowski, Andrzej. On the proportion of rank 0 twists of elliptic curves. Comptes Rendus. Mathématique, Volume 346 (2008) no. 9-10, pp. 483-486. doi : 10.1016/j.crma.2008.03.025. http://www.numdam.org/articles/10.1016/j.crma.2008.03.025/

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