Let E be an elliptic curve defined over Q, let denote its dth quadratic twist, and . We prove, that, for any positive integer k there are pairwise non-isogenous elliptic curves such that for a positive proportion of primes p.
Soit E une courbe elliptique définie sur Q, la tordue quadratique de E par d, et . On démontre qu'il existe, pour tout entier positif k, des courbes elliptiques , qui sont 2 à 2 non isogènes, et telles que pour une famille de nombres premiers p de densité positive.
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Andrzej Dąbrowski 1
@article{CRMATH_2008__346_9-10_483_0, author = {Andrzej D\k{a}browski}, title = {On the proportion of rank 0 twists of elliptic curves}, journal = {Comptes Rendus. Math\'ematique}, pages = {483--486}, publisher = {Elsevier}, volume = {346}, number = {9-10}, year = {2008}, doi = {10.1016/j.crma.2008.03.025}, language = {en}, }
Andrzej Dąbrowski. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.03.025/
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