Non-split Cartan case (reviewed)

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 $\F_p^*$.