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 **S4** means that $G$ is the full pre-image in $\GL(2,\F_p)$ of a subgroup (unique up to conjugacy) of $\PGL(2,\F_p)$ that is isomorphic to the symmetric group on
$4$ elements. This case can occur only if $p$ is congruent to $1$ modulo $4$.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by John Jones on 2018-06-18 03:46:46

**Referred to by:**

Not referenced anywhere at the moment.

**History:**(expand/hide all)

- 2018-06-18 03:46:46 by John Jones (Reviewed)