| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.9.18.1 |
$9$ |
$x^{9} + 3 x^{6} + 9 x^{5} + 18 x^{4} + 24 x^{3} + 9 x^{2} + 9 x + 21$ |
$3$ |
$9$ |
$1$ |
$18$ |
$D_{9}$ (as 9T3) |
$1$ |
$2$ |
$[3/2, 5/2]$ |
$[3/2, 5/2]_{2}$ |
$t + 1$ |
$x^{9} + 3 x^{6} + 9 x^{5} + 18 x^{4} + 24 x^{3} + 9 x^{2} + 9 x + 21$ |
$[10, 3, 0]$ |
$[1, 1]$ |
| 3.9.22.10 |
$9$ |
$x^{9} + 21 x^{6} + 18 x^{5} + 75$ |
$3$ |
$9$ |
$1$ |
$22$ |
$D_{9}$ (as 9T3) |
$2$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{2}$ |
$t + 1$ |
$x^{9} + 21 x^{6} + 18 x^{5} + 75$ |
$[14, 6, 0]$ |
$[2, 2]$ |
| 3.9.26.1 |
$9$ |
$x^{9} + 18 x^{6} + 54 x^{5} + 54 x^{4} + 54 x^{3} + 27 x^{2} + 30$ |
$3$ |
$9$ |
$1$ |
$26$ |
$D_{9}$ (as 9T3) |
$1$ |
$2$ |
$[5/2, 7/2]$ |
$[5/2, 7/2]_{2}$ |
$t + 1$ |
$x^{9} + 18 x^{6} + 54 x^{5} + 54 x^{4} + 54 x^{3} + 27 x^{2} + 30$ |
$[18, 9, 0]$ |
$[1, 1]$ |
| 3.9.26.2 |
$9$ |
$x^{9} + 54 x^{4} + 45 x^{3} + 54 x^{2} + 54 x + 12$ |
$3$ |
$9$ |
$1$ |
$26$ |
$D_{9}$ (as 9T3) |
$1$ |
$2$ |
$[5/2, 7/2]$ |
$[5/2, 7/2]_{2}$ |
$t + 1$ |
$x^{9} + 54 x^{4} + 45 x^{3} + 54 x^{2} + 54 x + 12$ |
$[18, 9, 0]$ |
$[1, 1]$ |
| 3.9.26.3 |
$9$ |
$x^{9} + 54 x^{2} + 3$ |
$3$ |
$9$ |
$1$ |
$26$ |
$D_{9}$ (as 9T3) |
$1$ |
$2$ |
$[5/2, 7/2]$ |
$[5/2, 7/2]_{2}$ |
$t + 1$ |
$x^{9} + 54 x^{2} + 3$ |
$[18, 9, 0]$ |
$[1, 1]$ |
