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

**Referred to by:**

**History:**(expand/hide all)

- 2019-05-21 11:51:22 by Andrew Sutherland (Reviewed)
- 2018-06-18 21:11:34 by John Jones (Reviewed)

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