Let $p$ be a prime and let $E$ be an elliptic curve defined over $\Q$. Assume that $p$ is a non-surjective prime for $E$.
Subgroups $G$ of $\GL(2,\F_p)$ that can arise as the image of the mod-$p$ Galois representation \[ \rho_{E,p}\colon {\Gal}(\overline{\Q}/\Q)\to \GL(2,\F_p) \] attached to $E$ are identified using the labels introduced by Sutherland in [arXiv:1504.07618, MR:3482279]. These labels have the form \[ \mathrm{\bf{S.a.b.c,}} \] where S is one B, Cs, Cn, Ns, Nn, or S4, and a, b, c are (optional) positive integers.
There are six cases: Borel B, split Cartan Cs, normalizer of the split Cartan Ns, nonsplit Cartan Cn, normalizer of the nonsplit Cartan Nn, exceptional S4.
Knowl status:
- Review status: reviewed
- Last edited by Andrew Sutherland on 2019-05-21 11:51:22
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- 2019-05-21 11:51:22 by Andrew Sutherland (Reviewed)
- 2018-06-18 21:11:34 by John Jones (Reviewed)