| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.9.9.2 |
$9$ |
$x^{9} - 3 x^{7} + 9 x^{6} - 9 x^{5} - 18 x^{4} + 81 x^{3} - 27 x^{2} - 27 x + 27$ |
$3$ |
$3$ |
$3$ |
$9$ |
$C_3^2 : S_3 $ (as 9T13) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.9.9.7 |
$9$ |
$x^{9} - 6 x^{7} + 9 x^{6} - 36 x^{5} - 36 x^{4} + 459 x^{3} - 108 x^{2} - 54 x + 27$ |
$3$ |
$3$ |
$3$ |
$9$ |
$C_3^2 : S_3 $ (as 9T13) |
$3$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.9.12.17 |
$9$ |
$x^{9} - 6 x^{8} - 36 x^{7} + 441 x^{6} + 126 x^{5} + 216 x^{4} + 189 x^{3} + 1404 x^{2} - 216$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3^2 : S_3 $ (as 9T13) |
$6$ |
$1$ |
$[2]$ |
$[2, 2]^{6}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6\right) x^{2} + 9 t + 3$ |
$[2, 0]$ |
$[2]$ |
| 3.9.15.4 |
$9$ |
$x^{9} - 18 x^{7} - 27 x^{6} + 324 x^{5} + 945 x^{4} + 17307 x^{3} + 26487 x^{2} + 11016 x + 432$ |
$3$ |
$3$ |
$3$ |
$15$ |
$C_3^2 : S_3 $ (as 9T13) |
$3$ |
$2$ |
$[5/2]$ |
$[3/2, 5/2]_{2}^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(18 t^{2} + 9 t + 18\right) x + 9 t^{2} + 9 t + 3$ |
$[3, 0]$ |
$[1]$ |
| 3.9.15.5 |
$9$ |
$x^{9} - 45 x^{7} + 27 x^{6} + 1863 x^{5} + 378 x^{4} + 10017 x^{3} + 44955 x^{2} + 25596 x + 7236$ |
$3$ |
$3$ |
$3$ |
$15$ |
$C_3^2 : S_3 $ (as 9T13) |
$3$ |
$2$ |
$[5/2]$ |
$[3/2, 5/2]_{2}^{3}$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(18 t^{2} + 18 t + 9\right) x + 9 t^{2} + 9 t + 21$ |
$[3, 0]$ |
$[1]$ |
| 3.9.18.40 |
$9$ |
$x^{9} + 6 x^{6} + 18 x + 21$ |
$3$ |
$9$ |
$1$ |
$18$ |
$C_3^2 : S_3 $ (as 9T13) |
$2$ |
$1$ |
$[2, 7/3]$ |
$[2, 2, 7/3]^{2}$ |
$t + 1$ |
$x^{9} + 6 x^{6} + 18 x + 21$ |
$[10, 6, 0]$ |
$[2, 1]$ |
| 3.9.18.41 |
$9$ |
$x^{9} + 6 x^{6} + 18 x + 12$ |
$3$ |
$9$ |
$1$ |
$18$ |
$C_3^2 : S_3 $ (as 9T13) |
$2$ |
$1$ |
$[2, 7/3]$ |
$[2, 2, 7/3]^{2}$ |
$t + 1$ |
$x^{9} + 6 x^{6} + 18 x + 12$ |
$[10, 6, 0]$ |
$[2, 1]$ |
| 3.9.18.42 |
$9$ |
$x^{9} + 6 x^{6} + 18 x + 3$ |
$3$ |
$9$ |
$1$ |
$18$ |
$C_3^2 : S_3 $ (as 9T13) |
$2$ |
$1$ |
$[2, 7/3]$ |
$[2, 2, 7/3]^{2}$ |
$t + 1$ |
$x^{9} + 6 x^{6} + 18 x + 3$ |
$[10, 6, 0]$ |
$[2, 1]$ |
| 3.9.19.7 |
$9$ |
$x^{9} + 6 x^{6} + 9 x^{2} + 3$ |
$3$ |
$9$ |
$1$ |
$19$ |
$C_3^2 : S_3 $ (as 9T13) |
$1$ |
$2$ |
$[2, 5/2]$ |
$[3/2, 2, 5/2]_{2}$ |
$t + 1$ |
$x^{9} + 6 x^{6} + 9 x^{2} + 3$ |
$[11, 6, 0]$ |
$[1, 1]$ |
| 3.9.19.8 |
$9$ |
$x^{9} + 6 x^{6} + 9 x^{2} + 12$ |
$3$ |
$9$ |
$1$ |
$19$ |
$C_3^2 : S_3 $ (as 9T13) |
$1$ |
$2$ |
$[2, 5/2]$ |
$[3/2, 2, 5/2]_{2}$ |
$t + 1$ |
$x^{9} + 6 x^{6} + 9 x^{2} + 12$ |
$[11, 6, 0]$ |
$[1, 1]$ |
| 3.9.19.9 |
$9$ |
$x^{9} + 6 x^{6} + 9 x^{2} + 21$ |
$3$ |
$9$ |
$1$ |
$19$ |
$C_3^2 : S_3 $ (as 9T13) |
$1$ |
$2$ |
$[2, 5/2]$ |
$[3/2, 2, 5/2]_{2}$ |
$t + 1$ |
$x^{9} + 6 x^{6} + 9 x^{2} + 21$ |
$[11, 6, 0]$ |
$[1, 1]$ |
| 3.9.21.55 |
$9$ |
$x^{9} + 18 x^{7} + 24 x^{6} + 9 x^{4} + 12$ |
$3$ |
$9$ |
$1$ |
$21$ |
$C_3^2 : S_3 $ (as 9T13) |
$1$ |
$2$ |
$[2, 17/6]$ |
$[2, 5/2, 17/6]_{2}$ |
$t + 1$ |
$x^{9} + 18 x^{7} + 24 x^{6} + 9 x^{4} + 12$ |
$[13, 6, 0]$ |
$[1, 1]$ |
| 3.9.21.56 |
$9$ |
$x^{9} + 9 x^{7} + 24 x^{6} + 9 x^{4} + 21$ |
$3$ |
$9$ |
$1$ |
$21$ |
$C_3^2 : S_3 $ (as 9T13) |
$1$ |
$2$ |
$[2, 17/6]$ |
$[2, 5/2, 17/6]_{2}$ |
$t + 1$ |
$x^{9} + 9 x^{7} + 24 x^{6} + 9 x^{4} + 21$ |
$[13, 6, 0]$ |
$[1, 1]$ |
| 3.9.21.57 |
$9$ |
$x^{9} + 18 x^{7} + 24 x^{6} + 9 x^{4} + 21$ |
$3$ |
$9$ |
$1$ |
$21$ |
$C_3^2 : S_3 $ (as 9T13) |
$1$ |
$2$ |
$[2, 17/6]$ |
$[2, 5/2, 17/6]_{2}$ |
$t + 1$ |
$x^{9} + 18 x^{7} + 24 x^{6} + 9 x^{4} + 21$ |
$[13, 6, 0]$ |
$[1, 1]$ |
| 3.9.21.58 |
$9$ |
$x^{9} + 6 x^{6} + 9 x^{4} + 3$ |
$3$ |
$9$ |
$1$ |
$21$ |
$C_3^2 : S_3 $ (as 9T13) |
$1$ |
$2$ |
$[2, 17/6]$ |
$[2, 5/2, 17/6]_{2}$ |
$t + 1$ |
$x^{9} + 6 x^{6} + 9 x^{4} + 3$ |
$[13, 6, 0]$ |
$[1, 1]$ |
| 3.9.21.59 |
$9$ |
$x^{9} + 18 x^{7} + 24 x^{6} + 9 x^{4} + 3$ |
$3$ |
$9$ |
$1$ |
$21$ |
$C_3^2 : S_3 $ (as 9T13) |
$1$ |
$2$ |
$[2, 17/6]$ |
$[2, 5/2, 17/6]_{2}$ |
$t + 1$ |
$x^{9} + 18 x^{7} + 24 x^{6} + 9 x^{4} + 3$ |
$[13, 6, 0]$ |
$[1, 1]$ |
| 3.9.21.60 |
$9$ |
$x^{9} + 9 x^{7} + 24 x^{6} + 9 x^{4} + 12$ |
$3$ |
$9$ |
$1$ |
$21$ |
$C_3^2 : S_3 $ (as 9T13) |
$1$ |
$2$ |
$[2, 17/6]$ |
$[2, 5/2, 17/6]_{2}$ |
$t + 1$ |
$x^{9} + 9 x^{7} + 24 x^{6} + 9 x^{4} + 12$ |
$[13, 6, 0]$ |
$[1, 1]$ |
| 3.9.21.61 |
$9$ |
$x^{9} + 9 x^{7} + 15 x^{6} + 9 x^{4} + 3$ |
$3$ |
$9$ |
$1$ |
$21$ |
$C_3^2 : S_3 $ (as 9T13) |
$1$ |
$2$ |
$[2, 17/6]$ |
$[2, 5/2, 17/6]_{2}$ |
$t + 1$ |
$x^{9} + 9 x^{7} + 15 x^{6} + 9 x^{4} + 3$ |
$[13, 6, 0]$ |
$[1, 1]$ |
| 3.9.21.62 |
$9$ |
$x^{9} + 24 x^{6} + 9 x^{4} + 21$ |
$3$ |
$9$ |
$1$ |
$21$ |
$C_3^2 : S_3 $ (as 9T13) |
$1$ |
$2$ |
$[2, 17/6]$ |
$[2, 5/2, 17/6]_{2}$ |
$t + 1$ |
$x^{9} + 24 x^{6} + 9 x^{4} + 21$ |
$[13, 6, 0]$ |
$[1, 1]$ |
| 3.9.21.63 |
$9$ |
$x^{9} + 9 x^{7} + 15 x^{6} + 9 x^{4} + 12$ |
$3$ |
$9$ |
$1$ |
$21$ |
$C_3^2 : S_3 $ (as 9T13) |
$1$ |
$2$ |
$[2, 17/6]$ |
$[2, 5/2, 17/6]_{2}$ |
$t + 1$ |
$x^{9} + 9 x^{7} + 15 x^{6} + 9 x^{4} + 12$ |
$[13, 6, 0]$ |
$[1, 1]$ |
