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 $E$.

Any label starting with **B** means that the group $G$ is contained in the Borel subgroup in $\GL(2,\F_p)$, i.e. a conjugate of the upper triangular group in $\GL(2,\F_p)$, and not contained in the subgroup of diagonal matrices.

The label **B** means that the group $G$ is the full Borel subgroup in $\GL(2,\F_p)$.

The label **B.a.b** means that the group $G$ is contained in the subgroup of the upper triangular group generated by the matrices
\[
\begin{pmatrix}a&0\\0&1/a\end{pmatrix}, \begin{pmatrix}b&0\\0&r/b\end{pmatrix}, \begin{pmatrix}1&1\\0&1\end{pmatrix}.
\]

where $r$ be the least positive integer that generates $\F_p^*$.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by John Cremona on 2019-03-28 05:59:13

**Referred to by:**

Not referenced anywhere at the moment.

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

- 2019-03-28 05:59:13 by John Cremona (Reviewed)
- 2018-06-18 12:00:58 by John Cremona (Reviewed)

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