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Let $E$ be an elliptic curve defined over $\Q$. A prime $p$ is called a surjective prime for $E$ if the mod-$p$ Galois representation \[ \rho_{E,p}: Gal(\overline{\Q}/\Q) \to \GL(2,\F_p) \] attached to $E$ is surjective.

Conjecturally, when $E$ does not have CM, all primes $p>37$ are surjective primes.

Knowl status:
  • Review status: reviewed
  • Last edited by John Jones on 2018-06-19 15:35:04
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