This is one of the six possible cases for the image of the mod $p$ Galois Representation if $p$ is a non-surjective prime for $E$.

The label **Cn** means that $G$ is contained in the nonsplit Cartan subgroup which is, up to conjugation, the unique maximal abelian subgroups of $\GL(2,\F_p)$ isomorphic to
$\F_{p^2}^*$.

For $p=2$ is the unique index 2 subgroup of $\GL(2,\F_2)$ and for $p$ odd consists of all matrices \[ \begin{pmatrix}x&ry\\y&x\end{pmatrix}, \] where $r$ be the least positive integer that generates $\F_p^*$.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by John Jones on 2018-06-19 18:54:21

**Referred to by:**

Not referenced anywhere at the moment.

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

- 2018-06-19 18:54:21 by John Jones (Reviewed)