| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.18.31 |
$12$ |
$x^{12} - 4 x^{11} + 22 x^{10} + 16 x^{9} + 50 x^{8} + 32 x^{7} + 144 x^{6} + 96 x^{5} + 236 x^{4} + 248 x^{2} + 248$ |
$2$ |
$4$ |
$3$ |
$18$ |
$A_4\times C_2$ (as 12T6) |
$3$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t\right) x^{3} + \left(2 t^{2} + 2 t + 2\right) x^{2} + 4 t + 6$ |
$[3, 2, 0]$ |
$[1]$ |
| 2.12.18.48 |
$12$ |
$x^{12} + 6 x^{11} + 18 x^{10} + 32 x^{9} + 34 x^{8} + 16 x^{7} - 8 x^{6} - 16 x^{5} - 12 x^{4} - 8 x^{3} - 8 x^{2} + 72$ |
$2$ |
$4$ |
$3$ |
$18$ |
$A_4\times C_2$ (as 12T6) |
$6$ |
$1$ |
$[2, 2]$ |
$[2, 2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{3} + 2 x^{2} + 4 t^{2} + 2$ |
$[3, 2, 0]$ |
$[1]$ |
| 2.12.18.52 |
$12$ |
$x^{12} + 10 x^{10} + 18 x^{8} - 8 x^{7} + 104 x^{6} + 48 x^{5} + 204 x^{4} + 216 x^{2} + 216$ |
$2$ |
$4$ |
$3$ |
$18$ |
$A_4\times C_2$ (as 12T6) |
$3$ |
$1$ |
$[2, 2]$ |
$[2, 2, 2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 t x^{3} + \left(2 t + 2\right) x^{2} + 6$ |
$[3, 2, 0]$ |
$[1]$ |
| 2.12.24.130 |
$12$ |
$x^{12} + 12 x^{11} + 54 x^{10} + 116 x^{9} + 162 x^{8} + 200 x^{7} + 640 x^{6} + 1792 x^{5} + 3964 x^{4} + 5536 x^{3} + 6360 x^{2} + 3888 x + 1944$ |
$2$ |
$4$ |
$3$ |
$24$ |
$A_4\times C_2$ (as 12T6) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t^{2} + 2 t + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 12 t^{2} + 12 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.182 |
$12$ |
$x^{12} - 8 x^{11} + 86 x^{10} + 52 x^{9} + 430 x^{8} + 1160 x^{7} + 800 x^{6} + 768 x^{5} + 1148 x^{4} + 336 x^{3} + 56 x^{2} - 336 x - 376$ |
$2$ |
$4$ |
$3$ |
$24$ |
$A_4\times C_2$ (as 12T6) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(6 t^{2} + 4 t + 6\right) x^{2} + \left(4 t + 4\right) x + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.280 |
$12$ |
$x^{12} + 12 x^{11} + 82 x^{10} + 260 x^{9} + 534 x^{8} + 968 x^{7} + 1280 x^{6} + 1376 x^{5} + 1740 x^{4} + 1376 x^{3} + 1096 x^{2} + 560 x - 1048$ |
$2$ |
$4$ |
$3$ |
$24$ |
$A_4\times C_2$ (as 12T6) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(6 t + 6\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 12 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.310 |
$12$ |
$x^{12} - 8 x^{11} + 98 x^{10} - 36 x^{9} + 338 x^{8} + 360 x^{7} + 1344 x^{6} + 1696 x^{5} + 3084 x^{4} + 2768 x^{3} + 1256 x^{2} + 1104 x + 536$ |
$2$ |
$4$ |
$3$ |
$24$ |
$A_4\times C_2$ (as 12T6) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(6 t + 6\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
