| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.14.13 |
$12$ |
$x^{12} + 12 x^{9} - 6 x^{8} + 30 x^{6} - 36 x^{5} + 45 x^{4} - 36 x^{3} + 54 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_3^2:C_{12}$ (as 12T73) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{3} + \left(6 t + 3\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.2 |
$12$ |
$x^{12} - 6 x^{9} + 6 x^{8} + 39 x^{6} + 18 x^{5} + 18 x^{4} + 54 x^{3} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_3^2:C_{12}$ (as 12T73) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{3} + \left(3 t + 6\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.16.10 |
$12$ |
$x^{12} + 12 x^{11} + 36 x^{10} + 30 x^{9} + 648 x^{8} + 1188 x^{7} + 4428 x^{6} + 5508 x^{5} + 20736 x^{4} + 5454 x^{3} + 40176 x^{2} + 25353$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:C_{12}$ (as 12T73) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 3 t^{2} x^{2} + 9 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.12 |
$12$ |
$x^{12} + 24 x^{11} + 216 x^{10} + 1128 x^{9} + 3996 x^{8} + 5184 x^{7} + 23382 x^{6} + 7776 x^{5} + 60264 x^{4} + 3024 x^{3} + 69660 x^{2} + 30213$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:C_{12}$ (as 12T73) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t^{2} + 6\right) x^{2} + 9 t^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.16 |
$12$ |
$x^{12} - 24 x^{11} + 306 x^{10} - 2688 x^{9} + 24057 x^{8} - 15336 x^{7} + 311742 x^{6} + 14256 x^{5} + 1525878 x^{4} + 117720 x^{3} + 3351780 x^{2} + 3379725$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:C_{12}$ (as 12T73) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 6 t + 3\right) x^{2} + 18 t^{3} + 18 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.17 |
$12$ |
$x^{12} - 24 x^{11} + 306 x^{10} - 2580 x^{9} + 22869 x^{8} - 7236 x^{7} + 99846 x^{6} - 4536 x^{5} + 179658 x^{4} + 3996 x^{3} + 191808 x^{2} + 110889$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:C_{12}$ (as 12T73) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 6 t + 3\right) x^{2} + 18 t^{3} + 18 t^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.21 |
$12$ |
$x^{12} + 6 x^{11} - 204 x^{9} - 891 x^{8} - 1134 x^{7} + 14796 x^{6} + 52326 x^{5} + 156978 x^{4} - 83970 x^{3} + 25920 x^{2} + 842805$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:C_{12}$ (as 12T73) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t + 3\right) x^{2} + 18 t^{3} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.3 |
$12$ |
$x^{12} - 12 x^{11} + 126 x^{10} - 474 x^{9} + 1539 x^{8} + 3510 x^{7} - 2214 x^{6} + 3240 x^{5} - 8100 x^{4} + 32670 x^{3} + 101250 x^{2} + 463725$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:C_{12}$ (as 12T73) |
$12$ |
$1$ |
$[2]$ |
$[2, 2]^{12}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 3\right) x^{2} + 18 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.45 |
$12$ |
$x^{12} + 24 x^{11} + 216 x^{10} + 1128 x^{9} + 4536 x^{8} + 12312 x^{7} + 43794 x^{6} + 32400 x^{5} + 163296 x^{4} + 14688 x^{3} + 156168 x^{2} + 82701$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:C_{12}$ (as 12T73) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t^{2} + 6\right) x^{2} + 9 t^{3} + 18 t^{2} + 18 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.9 |
$12$ |
$x^{12} - 24 x^{11} + 288 x^{10} - 1716 x^{9} + 5400 x^{8} - 3456 x^{7} + 25974 x^{6} - 1944 x^{5} + 103680 x^{4} - 11556 x^{3} + 341496 x^{2} + 411237$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:C_{12}$ (as 12T73) |
$12$ |
$1$ |
$[2]$ |
$[2, 2]^{12}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2}\right) x^{2} + 9 t^{3} + 9 t^{2} + 18 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.18.15 |
$12$ |
$x^{12} + 6 x^{11} + 15 x^{10} + 24 x^{9} + 36 x^{8} + 18 x^{7} - 15 x^{6} - 72 x^{5} + 54 x^{4} - 72 x^{3} + 585$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^2:C_{12}$ (as 12T73) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + \left(3 t + 6\right) x^{4} + 3 x^{3} + 21 t + 9$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.27 |
$12$ |
$x^{12} - 6 x^{11} + 24 x^{10} - 12 x^{9} + 90 x^{8} + 84 x^{6} + 36 x^{5} + 108 x^{4} + 72 x^{3} + 180$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^2:C_{12}$ (as 12T73) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{5} + \left(3 t + 6\right) x^{4} + 6 t x^{3} + 12 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.39 |
$12$ |
$x^{12} + 42 x^{10} + 48 x^{9} + 18 x^{8} + 36 x^{7} + 30 x^{6} + 36 x^{5} - 36 x^{3} + 18$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^2:C_{12}$ (as 12T73) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{5} + \left(3 t + 6\right) x^{4} + 6 x^{3} + 3 t$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.6 |
$12$ |
$x^{12} + 6 x^{10} + 6 x^{9} + 18 x^{8} + 18 x^{7} - 15 x^{6} + 54 x^{4} - 72 x^{3} + 585$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^2:C_{12}$ (as 12T73) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 6\right) x^{4} + 3 x^{3} + 21 t + 9$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.62 |
$12$ |
$x^{12} + 6 x^{11} + 24 x^{10} + 42 x^{9} + 36 x^{8} + 18 x^{7} - 15 x^{6} + 54 x^{5} + 54 x^{4} - 72 x^{3} + 585$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^2:C_{12}$ (as 12T73) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 6\right) x^{5} + \left(3 t + 6\right) x^{4} + 3 x^{3} + 21 t + 9$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.69 |
$12$ |
$x^{12} + 12 x^{11} + 42 x^{10} + 30 x^{9} - 18 x^{8} + 18 x^{7} + 39 x^{6} - 36 x^{5} + 54 x^{3} + 18$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3^2:C_{12}$ (as 12T73) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + \left(3 t + 6\right) x^{4} + \left(6 t + 3\right) x^{3} + 3 t$ |
$[4, 0]$ |
$[1, 1]$ |
