| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.9.12.4 |
$9$ |
$x^{9} + 6 x^{8} + 45 x^{7} + 252 x^{6} + 144 x^{5} + 540 x^{4} + 432 x^{3} + 864 x^{2} + 1728$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3^2:C_3$ (as 9T7) |
$3$ |
$1$ |
$[2]$ |
$[2, 2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 3 t + 6\right) x^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
| 3.9.16.1 |
$9$ |
$x^{9} + 3 x^{8} + 3 x^{6} + 3$ |
$3$ |
$9$ |
$1$ |
$16$ |
$C_3^2:C_3$ (as 9T7) |
$3$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{3}$ |
$t + 1$ |
$x^{9} + 3 x^{8} + 3 x^{6} + 3$ |
$[8, 6, 0]$ |
$[3]$ |
| 3.9.16.2 |
$9$ |
$x^{9} + 3 x^{8} + 3 x^{6} + 21$ |
$3$ |
$9$ |
$1$ |
$16$ |
$C_3^2:C_3$ (as 9T7) |
$3$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{3}$ |
$t + 1$ |
$x^{9} + 3 x^{8} + 3 x^{6} + 21$ |
$[8, 6, 0]$ |
$[3]$ |
| 3.9.16.3 |
$9$ |
$x^{9} + 3 x^{8} + 3 x^{6} + 12$ |
$3$ |
$9$ |
$1$ |
$16$ |
$C_3^2:C_3$ (as 9T7) |
$3$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{3}$ |
$t + 1$ |
$x^{9} + 3 x^{8} + 3 x^{6} + 12$ |
$[8, 6, 0]$ |
$[3]$ |
