Geodesic
On the Surjectivity of the Galois Representations Associated to Non-CM Elliptic Curves
Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 16-31

Voir la notice de l'article provenant de la source Cambridge University Press

Let $E$ be an elliptic curve defined over $\mathbb{Q}$ , of conductor $N$ and without complex multiplication. For any positive integer $l$ , let ${{\phi }_{1}}$ be the Galois representation associated to the $l$ -division points of $E$ . From a celebrated 1972 result of Serre we know that ${{\phi }_{1}}$ is surjective for any sufficiently large prime $l$ . In this paper we find conditional and unconditional upper bounds in terms of $N$ for the primes $l$ for which ${{\phi }_{1}}$ is not surjective.
DOI : 10.4153/CMB-2005-002-x
Mots-clés : 11G05, 11N36, 11R45 
Cojocaru, Alina Carmen; Kani, Ernst. On the Surjectivity of the Galois Representations Associated to Non-CM Elliptic Curves. Canadian mathematical bulletin, Tome 48 (2005) no. 1, pp. 16-31. doi: 10.4153/CMB-2005-002-x
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