| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.14.5 |
$12$ |
$x^{12} + 6 x^{6} + 36 x^{4} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.18.42 |
$12$ |
$x^{12} + 15 x^{10} + 27 x^{8} + 15 x^{6} + 18 x^{4} + 9$ |
$3$ |
$6$ |
$2$ |
$18$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{5} + 3 x^{4} + \left(3 t + 3\right) x^{3} + 3$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.78 |
$12$ |
$x^{12} - 6 x^{11} + 24 x^{10} - 30 x^{9} + 81 x^{8} - 36 x^{7} + 60 x^{6} + 90 x^{5} - 36 x^{4} + 180 x^{3} + 117$ |
$3$ |
$6$ |
$2$ |
$18$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{5} + 3 x^{4} + 6 t x^{3} + 9 t + 3$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.22.38 |
$12$ |
$x^{12} - 42 x^{9} - 18 x^{8} - 18 x^{7} + 1023 x^{6} + 810 x^{5} + 972 x^{4} + 630 x^{3} + 270 x^{2} + 108 x + 90$ |
$3$ |
$6$ |
$2$ |
$22$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[5/2]$ |
$[3/2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(24 t + 3\right) x^{3} + 9 t x^{2} + 9 t x + 9 t + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.40 |
$12$ |
$x^{12} - 6 x^{9} + 36 x^{7} + 240 x^{6} + 270 x^{5} - 27 x^{4} + 522 x^{3} + 648 x^{2} + 108 x + 333$ |
$3$ |
$6$ |
$2$ |
$22$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(15 t + 12\right) x^{3} + \left(9 t + 9\right) x^{2} + 18 x + 18 t + 21$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.79 |
$12$ |
$x^{12} + 42 x^{9} + 18 x^{7} + 465 x^{6} + 702 x^{4} + 504 x^{3} + 81 x^{2} + 216 x + 144$ |
$3$ |
$6$ |
$2$ |
$22$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[5/2]$ |
$[3/2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 21 x^{3} + \left(18 t + 18\right) x^{2} + 9 x + 12$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.81 |
$12$ |
$x^{12} + 36 x^{8} + 618 x^{6} + 324 x^{4} + 756 x^{2} + 441$ |
$3$ |
$6$ |
$2$ |
$22$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(24 t + 24\right) x^{3} + 18 x^{2} + 21$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.90 |
$12$ |
$x^{12} - 42 x^{9} + 18 x^{8} + 36 x^{7} + 1023 x^{6} + 54 x^{5} - 594 x^{4} + 1062 x^{3} + 702 x^{2} + 108 x + 333$ |
$3$ |
$6$ |
$2$ |
$22$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[5/2]$ |
$[2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(24 t + 3\right) x^{3} + \left(9 t + 18\right) x^{2} + 18 x + 18 t + 21$ |
$[6, 0]$ |
$[1, 1]$ |
| 3.12.22.91 |
$12$ |
$x^{12} + 36 x^{9} - 18 x^{8} + 357 x^{6} - 270 x^{5} + 270 x^{4} + 756 x^{3} + 108 x^{2} + 144$ |
$3$ |
$6$ |
$2$ |
$22$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[5/2]$ |
$[3/2, 5/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 21\right) x^{3} + 9 t x^{2} + \left(18 t + 18\right) x + 12$ |
$[6, 0]$ |
$[1, 1]$ |
