Let $p$ be a prime and let $E$ be an elliptic curve defined over a number field $K$.

Subgroups $G$ of $\GL(2,\F_p)$ that can arise as the image of the mod-$p$ Galois representation
\[
\rho_{E,p}\colon {\Gal}(\overline{K}/K)\to \GL(2,\F_p)
\]
attached to $E$ that do not contain $\SL(2,\F_p)$ are identified using the labels introduced by Sutherland in [MR:3482279]. These labels have the form
\[
\mathrm{\bf{S.a.b.c[d],}}
\]
where **S** is one **B**, **Cs**, **Cn**, **Ns**, **Nn**, **A4**, **S4**, or **A5** and **a**, **b**, **c**, **d** are (optional) nonnegative 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 **A4**, **S4**, **A5**.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by John Jones on 2018-06-18 16:36:35

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

- 2018-06-18 16:36:35 by John Jones (Reviewed)