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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 $\F_p^*$.

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