| Label |
$n$ |
Polynomial |
$p$ |
$f$ |
$e$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible Artin slopes |
Visible Swan slopes |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
$\#\Aut(K/\Q_p)$ |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 2.2.8.32c8.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.Q_{16}$ (as 16T702) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{4}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{4}$ |
$[2,2,\frac{5}{2}]^{2}$ |
$[1,1,\frac{3}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 2 x^{4} + 4 x^{3} + 4 x + 6$ |
$[9, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.32c8.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 6 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.Q_{16}$ (as 16T702) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{4}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{4}$ |
$[2,2,\frac{5}{2}]^{2}$ |
$[1,1,\frac{3}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 6 x^{4} + 4 x^{3} + 4 x + 6$ |
$[9, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.32c8.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.Q_{16}$ (as 16T702) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{4}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{4}$ |
$[2,2,\frac{5}{2}]^{2}$ |
$[1,1,\frac{3}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 2 x^{4} + 4 x^{3} + 4 x + 2$ |
$[9, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.32c8.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 6 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^4.Q_{16}$ (as 16T702) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{5}{2}, \frac{5}{2}]^{4}$ |
$[1,1,1,1,\frac{3}{2},\frac{3}{2}]^{4}$ |
$[2,2,\frac{5}{2}]^{2}$ |
$[1,1,\frac{3}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 6 x^{4} + 4 x^{3} + 4 x + 2$ |
$[9, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
