Normalizer of the split Cartan case
This is one of the six possible cases for the {{ KNOWL('ec.q.galois_rep_image', 'image of the mod $p$ Galois Representation')}} if $p$ is a {{ KNOWL('ec.q.non-surjective_prime', 'non-surjective prime')}} for an elliptic curve $E$. The label **Ns** means that $G$ is contained in the normalizer of the split Cartan subgroup but not in the split Cartan subgroup itself. The label **Ns.a.b** means that $G$ is contained in the subgroup of the normalizer of the split Cartan subgroug generated by \[ \begin{pmatrix}a&0\\0&1/a\end{pmatrix}, \begin{pmatrix}0&b\\-r/b&0\end{pmatrix}, \] where $r$ be the least positive integer that generates $\F_p^*$. The label **Ns.a.b.c** means that $G$ is contained in the subgroup of the normalizer of the split Cartan subgroup generated by \[ \begin{pmatrix}a&0\\0&1/a\end{pmatrix}, \begin{pmatrix}0&b\\-1/b&0\end{pmatrix}, \begin{pmatrix}0&c\\-r/c&0\end{pmatrix} \] where $r$ be the least positive integer that generates $\F_p^*$. Conjecturally, this case arises only when $E$ has CM.
The L-functions and modular forms database: Normalizer of the split Cartan case