show · ec.q.non-surjective_prime all knowls · up · search:

Let $E$ be an elliptic curve defined over $\Q$. A prime $p$ is called a non-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 not surjective.

There are only finitely many non-surjective primes for any elliptic curve without CM by a result of Serre. Conjecturally, the largest possible non-surjective prime is $37$.

Authors:
Knowl status:
  • Review status: reviewed
  • Last edited by John Jones on 2018-06-19 18:53:33
Referred to by:
History: (expand/hide all)