| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.14.11 |
$12$ |
$x^{12} + 12 x^{11} + 72 x^{10} + 280 x^{9} + 792 x^{8} + 1728 x^{7} + 2918 x^{6} + 3684 x^{5} + 3156 x^{4} + 1376 x^{3} - 36 x^{2} - 168 x + 25$ |
$3$ |
$6$ |
$2$ |
$14$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.6 |
$12$ |
$x^{12} + 6 x^{8} + 15 x^{6} + 9 x^{4} + 18 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.18.85 |
$12$ |
$x^{12} + 24 x^{11} + 246 x^{10} + 1468 x^{9} + 5901 x^{8} + 17052 x^{7} + 36566 x^{6} + 58896 x^{5} + 70926 x^{4} + 62060 x^{3} + 37140 x^{2} + 13680 x + 2425$ |
$3$ |
$6$ |
$2$ |
$18$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[2]$ |
$[2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + 3 x^{4} + 6 x^{3} + 3$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.22.44 |
$12$ |
$x^{12} + 105 x^{6} + 144$ |
$3$ |
$6$ |
$2$ |
$22$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(9 t + 9\right) x^{3} + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.67 |
$12$ |
$x^{12} + 12 x^{11} + 72 x^{10} + 280 x^{9} + 816 x^{8} + 1920 x^{7} + 3512 x^{6} + 4560 x^{5} + 3444 x^{4} + 272 x^{3} - 720 x^{2} + 960 x + 928$ |
$3$ |
$6$ |
$2$ |
$22$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{2} + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.96 |
$12$ |
$x^{12} + 30 x^{9} + 36 x^{7} + 231 x^{6} + 621 x^{4} + 90 x^{3} + 486 x^{2} + 108 x + 90$ |
$3$ |
$6$ |
$2$ |
$22$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[5/2]$ |
$[5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 15 x^{3} + \left(9 t + 9\right) x^{2} + 18 x + 9 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
