| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.20.47 |
$12$ |
$x^{12} + 6 x^{11} + 9 x^{10} - 6 x^{9} + 18 x^{8} + 108 x^{7} + 42 x^{6} - 36 x^{5} + 324 x^{4} - 72 x^{3} + 432 x^{2} + 144$ |
$3$ |
$6$ |
$2$ |
$20$ |
$C_3^4:D_4$ (as 12T172) |
$2$ |
$4$ |
$[9/4]$ |
$[5/4, 5/4, 9/4, 9/4]_{4}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + 3 t x^{3} + 18 x^{2} + 12$ |
$[5, 0]$ |
$[1, 1]$ |
| 3.12.20.48 |
$12$ |
$x^{12} + 9 x^{10} + 18 x^{8} + 54 x^{7} + 123 x^{6} + 108 x^{5} + 189 x^{4} + 378 x^{3} + 486 x^{2} + 324 x + 90$ |
$3$ |
$6$ |
$2$ |
$20$ |
$C_3^4:D_4$ (as 12T172) |
$2$ |
$4$ |
$[9/4]$ |
$[5/4, 5/4, 9/4, 9/4]_{4}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{5} + \left(3 t + 3\right) x^{3} + \left(9 t + 9\right) x^{2} + \left(18 t + 18\right) x + 9 t + 12$ |
$[5, 0]$ |
$[1, 1]$ |
| 3.12.20.52 |
$12$ |
$x^{12} + 12 x^{11} + 36 x^{10} - 18 x^{8} - 108 x^{7} + 15 x^{6} + 144 x^{5} + 459 x^{4} + 378 x^{3} + 351 x^{2} + 162 x + 90$ |
$3$ |
$6$ |
$2$ |
$20$ |
$C_3^4:D_4$ (as 12T172) |
$2$ |
$4$ |
$[9/4]$ |
$[5/4, 5/4, 9/4, 9/4]_{4}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + \left(3 t + 3\right) x^{3} + \left(18 t + 9\right) x^{2} + \left(9 t + 9\right) x + 9 t + 12$ |
$[5, 0]$ |
$[1, 1]$ |
| 3.12.20.55 |
$12$ |
$x^{12} + 6 x^{11} + 9 x^{10} + 24 x^{6} + 72 x^{5} + 189 x^{4} + 378 x^{3} + 405 x^{2} + 324 x + 360$ |
$3$ |
$6$ |
$2$ |
$20$ |
$C_3^4:D_4$ (as 12T172) |
$2$ |
$4$ |
$[9/4]$ |
$[5/4, 5/4, 9/4, 9/4]_{4}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + \left(6 t + 6\right) x^{3} + \left(9 t + 9\right) x^{2} + \left(9 t + 9\right) x + 18 t + 12$ |
$[5, 0]$ |
$[1, 1]$ |
| 3.12.20.60 |
$12$ |
$x^{12} + 9 x^{10} + 12 x^{9} + 36 x^{8} + 150 x^{6} + 324 x^{5} + 324 x^{4} + 36 x^{3} + 432 x^{2} + 648 x + 333$ |
$3$ |
$6$ |
$2$ |
$20$ |
$C_3^4:D_4$ (as 12T172) |
$2$ |
$4$ |
$[9/4]$ |
$[5/4, 5/4, 9/4, 9/4]_{4}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{5} + 6 x^{3} + 18 x^{2} + \left(18 t + 18\right) x + 18 t + 21$ |
$[5, 0]$ |
$[1, 1]$ |
| 3.12.20.61 |
$12$ |
$x^{12} + 9 x^{10} - 12 x^{9} + 36 x^{8} + 36 x^{7} + 114 x^{6} - 216 x^{4} - 252 x^{3} + 324 x^{2} + 756 x + 441$ |
$3$ |
$6$ |
$2$ |
$20$ |
$C_3^4:D_4$ (as 12T172) |
$2$ |
$4$ |
$[9/4]$ |
$[5/4, 5/4, 9/4, 9/4]_{4}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{5} + 6 t x^{3} + 18 x + 21$ |
$[5, 0]$ |
$[1, 1]$ |
