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Let $p$ be a prime and let $E$ be an elliptic curve defined over a number field $K$.

Subgroups $G$ of $\GL(2,\F_p)$ that can arise as the image of the mod-$p$ Galois representation $\rho_{E,p}\colon {\Gal}(\overline{K}/K)\to \GL(2,\F_p)$ attached to $E$ that do not contain $\SL(2,\F_p)$ are identified using the labels introduced by Sutherland in [MR:3482279]. These labels have the form $\mathrm{\bf{S.a.b.c[d],}}$ where S is one B, Cs, Cn, Ns, Nn, A4, S4, or A5 and a, b, c, d are (optional) nonnegative integers.

There are six cases: Borel B, split Cartan Cs, normalizer of the split Cartan Ns, nonsplit Cartan Cn, normalizer of the nonsplit Cartan Nn, exceptional A4, S4, A5.

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• Review status: reviewed
• Last edited by John Jones on 2018-06-18 16:36:35
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