| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.12.26 |
$12$ |
$x^{12} + 12 x^{11} + 98 x^{10} + 542 x^{9} + 2359 x^{8} + 7956 x^{7} + 21831 x^{6} + 47308 x^{5} + 82476 x^{4} + 109442 x^{3} + 112071 x^{2} + 76900 x + 33205$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$1$ |
$[2]$ |
$[2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 2 x + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.18.15 |
$12$ |
$x^{12} - 12 x^{11} - 56 x^{9} + 2372 x^{8} + 8992 x^{7} + 115648 x^{6} + 164160 x^{5} + 1305648 x^{4} - 282560 x^{3} + 5591296 x^{2} - 9640320 x + 8497856$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$1$ |
$[3]$ |
$[3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2}\right) x + 8 t^{5} + 4 t^{3} + 4 t^{2} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.23 |
$12$ |
$x^{12} - 12 x^{11} + 48 x^{10} - 344 x^{9} + 8244 x^{8} - 31136 x^{7} + 54848 x^{6} - 23104 x^{5} + 18864 x^{4} - 7360 x^{3} + 5120 x^{2} + 5760 x + 1472$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$1$ |
$[3]$ |
$[3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t\right) x + 4 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.12.24.307 |
$12$ |
$x^{12} - 8 x^{11} + 98 x^{10} - 148 x^{9} + 518 x^{8} + 320 x^{7} + 480 x^{6} + 1120 x^{5} + 612 x^{4} + 2080 x^{3} - 312 x^{2} - 144 x + 1944$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_6\times C_2$ (as 12T2) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + 6 x^{2} + 4 x + 12 t^{2} + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.315 |
$12$ |
$x^{12} - 8 x^{11} + 78 x^{10} + 76 x^{9} - 30 x^{8} + 720 x^{7} + 1200 x^{6} + 1248 x^{5} + 2676 x^{4} + 3712 x^{3} + 3448 x^{2} + 2160 x + 4072$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_6\times C_2$ (as 12T2) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 4 t + 2\right) x^{2} + 4 x + 12 t^{2} + 12 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.318 |
$12$ |
$x^{12} + 10 x^{10} + 12 x^{9} + 110 x^{8} + 80 x^{7} + 752 x^{6} + 512 x^{5} + 1636 x^{4} + 1504 x^{3} + 1224 x^{2} + 1008 x - 648$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_6\times C_2$ (as 12T2) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 6\right) x^{2} + 4 x + 12 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.79 |
$12$ |
$x^{12} - 8 x^{11} + 14 x^{10} + 76 x^{9} + 138 x^{8} + 432 x^{7} + 688 x^{6} + 992 x^{5} + 1748 x^{4} + 1728 x^{3} + 1848 x^{2} + 1648 x + 968$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_6\times C_2$ (as 12T2) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(4 t^{2} + 2\right) x^{2} + 4 x + 12 t^{2} + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
