| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.12.18 |
$12$ |
$x^{12} - 36 x^{11} + 438 x^{10} + 120 x^{9} - 4563 x^{8} + 1188 x^{7} + 22410 x^{6} + 10692 x^{5} - 17658 x^{4} - 3780 x^{3} + 6804 x^{2} - 1296 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$F_9$ (as 12T46) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3\right) x^{2} + 6 t^{3} x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.4 |
$12$ |
$x^{12} - 24 x^{11} + 192 x^{10} + 1236 x^{9} + 2160 x^{8} + 7560 x^{7} + 29430 x^{6} + 30456 x^{5} + 6804 x^{4} - 540 x^{3} + 1296 x^{2} - 648 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$F_9$ (as 12T46) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6\right) x^{2} + \left(3 t^{3} + 3 t^{2} + 6 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.16.19 |
$12$ |
$x^{12} - 24 x^{11} + 216 x^{10} - 1392 x^{9} + 10908 x^{8} - 6480 x^{7} + 92880 x^{6} - 7776 x^{5} + 264384 x^{4} - 8640 x^{3} + 207360 x^{2} + 51840$ |
$3$ |
$3$ |
$4$ |
$16$ |
$F_9$ (as 12T46) |
$8$ |
$1$ |
$[2]$ |
$[2, 2]^{8}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 6 t\right) x^{2} + 18 t^{3} + 12$ |
$[2, 0]$ |
$[2]$ |
| 3.12.16.6 |
$12$ |
$x^{12} - 30 x^{11} + 432 x^{10} - 3282 x^{9} + 15012 x^{8} - 14580 x^{7} + 93204 x^{6} - 21870 x^{5} + 238140 x^{4} - 11070 x^{3} + 281070 x^{2} + 128385$ |
$3$ |
$3$ |
$4$ |
$16$ |
$F_9$ (as 12T46) |
$8$ |
$1$ |
$[2]$ |
$[2, 2]^{8}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 3 t\right) x^{2} + 9 t^{3} + 9 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[2]$ |
