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# Surjectivity of $\mod\ell$ Representations Attached to Elliptic Curves and Congruence Primes

Published:2002-09-01
Printed: Sep 2002
• Imin Chen
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## Abstract

For a modular elliptic curve $E/\mathbb{Q}$, we show a number of links between the primes $\ell$ for which the mod $\ell$ representation of $E/\mathbb{Q}$ has projective dihedral image and congruence primes for the newform associated to $E/\mathbb{Q}$.
 Keywords: torsion points of elliptic curves, Galois representations, congruence primes, Serre tori, grossencharacters, non-split Cartan
 MSC Classifications: 11G05 - Elliptic curves over global fields [See also 14H52] 11F80 - Galois representations