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Critère d'irréductibilité pour les courbes elliptiques semi-stables sur un corps de nombres

For a fixed number field and an elliptic curve defined and semi-stable over this number field, we consider the set of prime numbers p such that the Galois representation attached to the p-torsion points of the elliptic curve is reducible. When the number field satisfies a certain necessary condition, we give an explicit bound, depending only on the number field and not on the semi-stable elliptic curve, for these primes. This generalizes previous results of Kraus.

preprint2012arXivOpen access
Agnès David
math.NT
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Agnès David

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