| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.9.0.1 |
$9$ |
$x^{9} + 2 x^{3} + 2 x^{2} + x + 1$ |
$3$ |
$1$ |
$9$ |
$0$ |
$C_9$ (as 9T1) |
$9$ |
$1$ |
$[\ ]$ |
$[\ ]^{9}$ |
$t^{9} + 2 t^{3} + 2 t^{2} + t + 1$ |
$x - 3$ |
$[0]$ |
$[]$ |
| 3.9.12.2 |
$9$ |
$x^{9} + 18 x^{8} + 108 x^{7} + 243 x^{6} + 324 x^{5} + 972 x^{4} + 1269 x^{3} + 7614 x^{2} + 15984$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9$ (as 9T1) |
$3$ |
$1$ |
$[2]$ |
$[2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 6 x^{2} + 9 t^{2} + 18 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.9.12.3 |
$9$ |
$x^{9} + 18 x^{8} + 108 x^{7} + 153 x^{6} - 756 x^{5} - 2268 x^{4} + 891 x^{3} + 5346 x^{2} + 9099$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9$ (as 9T1) |
$3$ |
$1$ |
$[2]$ |
$[2]^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 6 x^{2} + 18 t^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.9.22.1 |
$9$ |
$x^{9} + 9 x^{8} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 66$ |
$3$ |
$9$ |
$1$ |
$22$ |
$C_9$ (as 9T1) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{9} + 9 x^{8} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 66$ |
$[14, 6, 0]$ |
$[1, 1]$ |
| 3.9.22.2 |
$9$ |
$x^{9} + 9 x^{7} + 24 x^{6} + 18 x^{5} + 30$ |
$3$ |
$9$ |
$1$ |
$22$ |
$C_9$ (as 9T1) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{9} + 9 x^{7} + 24 x^{6} + 18 x^{5} + 30$ |
$[14, 6, 0]$ |
$[1, 1]$ |
| 3.9.22.3 |
$9$ |
$x^{9} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 12$ |
$3$ |
$9$ |
$1$ |
$22$ |
$C_9$ (as 9T1) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{9} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 12$ |
$[14, 6, 0]$ |
$[1, 1]$ |
| 3.9.22.4 |
$9$ |
$x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 48$ |
$3$ |
$9$ |
$1$ |
$22$ |
$C_9$ (as 9T1) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 48$ |
$[14, 6, 0]$ |
$[1, 1]$ |
| 3.9.22.5 |
$9$ |
$x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 21$ |
$3$ |
$9$ |
$1$ |
$22$ |
$C_9$ (as 9T1) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 21$ |
$[14, 6, 0]$ |
$[1, 1]$ |
| 3.9.22.6 |
$9$ |
$x^{9} + 18 x^{8} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 57$ |
$3$ |
$9$ |
$1$ |
$22$ |
$C_9$ (as 9T1) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{9} + 18 x^{8} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 57$ |
$[14, 6, 0]$ |
$[1, 1]$ |
| 3.9.22.7 |
$9$ |
$x^{9} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 39$ |
$3$ |
$9$ |
$1$ |
$22$ |
$C_9$ (as 9T1) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{9} + 15 x^{6} + 18 x^{5} + 9 x^{3} + 39$ |
$[14, 6, 0]$ |
$[1, 1]$ |
| 3.9.22.8 |
$9$ |
$x^{9} + 24 x^{6} + 18 x^{5} + 9 x^{3} + 3$ |
$3$ |
$9$ |
$1$ |
$22$ |
$C_9$ (as 9T1) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{9} + 24 x^{6} + 18 x^{5} + 9 x^{3} + 3$ |
$[14, 6, 0]$ |
$[1, 1]$ |
| 3.9.22.9 |
$9$ |
$x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 75$ |
$3$ |
$9$ |
$1$ |
$22$ |
$C_9$ (as 9T1) |
$1$ |
$1$ |
$[2, 3]$ |
$[2, 3]$ |
$t + 1$ |
$x^{9} + 9 x^{7} + 6 x^{6} + 18 x^{5} + 75$ |
$[14, 6, 0]$ |
$[1, 1]$ |
