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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 Cs means that the group $G$ is contained in the full split Cartan subgroup of $\GL(2,\F_p)$, i.e., up to conjugation, the unique maximal abelian subgroup of $\GL(2,\F_p)$ isomorphic to $\F_p^\times\times\F_p^\times$.

The label Cs.a.b means that the group $G$ is contained in the subgroup of the full split Cartan subgroup generated by \[ \begin{pmatrix}a&0\\0&1/a\end{pmatrix}, \begin{pmatrix}b&0\\0&r/b\end{pmatrix}. \] where $r$ is the least positive integer that generates $(\Z/p\Z)^\times\simeq \F_p^\times$.

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  • Review status: reviewed
  • Last edited by John Jones on 2018-06-19 15:37:01
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