show · ec.galois_rep_image all knowls · up · search:

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.

Authors:
Knowl status:
  • Review status: reviewed
  • Last edited by John Jones on 2018-06-18 16:36:35
Referred to by:
History: (expand/hide all)