Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
3.9.12.24 |
$9$ |
$x^{9} + 3 x^{4} + 3$ |
$3$ |
$9$ |
$1$ |
$12$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[3/2, 3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t + 1$ |
$x^{9} + 3 x^{4} + 3$ |
$[4, 4, 0]$ |
$[2]$ |
3.9.15.15 |
$9$ |
$x^{9} + 6 x^{8} + 3 x^{7} + 3 x^{3} + 21$ |
$3$ |
$9$ |
$1$ |
$15$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[3/2, 2]$ |
$[3/2, 2]_{2}^{2}$ |
$t + 1$ |
$x^{9} + 6 x^{8} + 3 x^{7} + 3 x^{3} + 21$ |
$[7, 3, 0]$ |
$[2, 1]$ |
3.9.15.30 |
$9$ |
$x^{9} + 3 x^{8} + 6 x^{7} + 6 x^{6} + 6 x^{3} + 12$ |
$3$ |
$9$ |
$1$ |
$15$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[3/2, 2]$ |
$[3/2, 2]_{2}^{2}$ |
$t + 1$ |
$x^{9} + 3 x^{8} + 6 x^{7} + 6 x^{6} + 6 x^{3} + 12$ |
$[7, 3, 0]$ |
$[2, 1]$ |
3.9.18.34 |
$9$ |
$x^{9} + 3 x^{6} + 18 x^{5} + 18 x^{4} + 15 x^{3} + 18 x^{2} + 18 x + 12$ |
$3$ |
$9$ |
$1$ |
$18$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[3/2, 5/2]$ |
$[3/2, 5/2]_{2}^{2}$ |
$t + 1$ |
$x^{9} + 3 x^{6} + 18 x^{5} + 18 x^{4} + 15 x^{3} + 18 x^{2} + 18 x + 12$ |
$[10, 3, 0]$ |
$[1, 1]$ |
3.9.18.35 |
$9$ |
$x^{9} + 9 x^{5} + 9 x^{4} + 6 x^{3} + 9 x^{2} + 18 x + 21$ |
$3$ |
$9$ |
$1$ |
$18$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[3/2, 5/2]$ |
$[3/2, 5/2]_{2}^{2}$ |
$t + 1$ |
$x^{9} + 9 x^{5} + 9 x^{4} + 6 x^{3} + 9 x^{2} + 18 x + 21$ |
$[10, 3, 0]$ |
$[1, 1]$ |
3.9.18.36 |
$9$ |
$x^{9} + 3 x^{6} + 9 x^{4} + 15 x^{3} + 18 x^{2} + 18 x + 21$ |
$3$ |
$9$ |
$1$ |
$18$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[3/2, 5/2]$ |
$[3/2, 5/2]_{2}^{2}$ |
$t + 1$ |
$x^{9} + 3 x^{6} + 9 x^{4} + 15 x^{3} + 18 x^{2} + 18 x + 21$ |
$[10, 3, 0]$ |
$[1, 1]$ |
3.9.19.1 |
$9$ |
$x^{9} + 3 x^{6} + 18 x^{5} + 18 x^{4} + 18 x^{3} + 9 x^{2} + 3$ |
$3$ |
$9$ |
$1$ |
$19$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[2, 5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t + 1$ |
$x^{9} + 3 x^{6} + 18 x^{5} + 18 x^{4} + 18 x^{3} + 9 x^{2} + 3$ |
$[11, 6, 0]$ |
$[1, 2]$ |
3.9.19.2 |
$9$ |
$x^{9} + 3 x^{6} + 9 x^{2} + 3$ |
$3$ |
$9$ |
$1$ |
$19$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[2, 5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t + 1$ |
$x^{9} + 3 x^{6} + 9 x^{2} + 3$ |
$[11, 6, 0]$ |
$[1, 2]$ |
3.9.19.3 |
$9$ |
$x^{9} + 3 x^{6} + 9 x^{2} + 21$ |
$3$ |
$9$ |
$1$ |
$19$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[2, 5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t + 1$ |
$x^{9} + 3 x^{6} + 9 x^{2} + 21$ |
$[11, 6, 0]$ |
$[1, 2]$ |