| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.0.1 |
$12$ |
$x^{12} + x^{6} + x^{5} + x^{4} + x^{2} + 2$ |
$3$ |
$1$ |
$12$ |
$0$ |
$C_{12}$ (as 12T1) |
$12$ |
$1$ |
$[\ ]$ |
$[\ ]^{12}$ |
$t^{12} + t^{6} + t^{5} + t^{4} + t^{2} + 2$ |
$x - 3$ |
$[0]$ |
$[]$ |
| 3.12.6.1 |
$12$ |
$x^{12} + 18 x^{8} + 81 x^{4} - 486 x^{2} + 1458$ |
$3$ |
$2$ |
$6$ |
$6$ |
$C_{12}$ (as 12T1) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$t^{6} + 2 t^{4} + t^{2} + 2 t + 2$ |
$x^{2} + 3 t$ |
$[0]$ |
$[1]$ |
| 3.12.6.2 |
$12$ |
$x^{12} + 22 x^{10} + 177 x^{8} + 4 x^{7} + 644 x^{6} - 100 x^{5} + 876 x^{4} - 224 x^{3} + 1076 x^{2} + 344 x + 112$ |
$3$ |
$2$ |
$6$ |
$6$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$t^{6} + 2 t^{4} + t^{2} + 2 t + 2$ |
$x^{2} + 3$ |
$[0]$ |
$[1]$ |
| 3.12.9.1 |
$12$ |
$x^{12} + 18 x^{4} - 27$ |
$3$ |
$4$ |
$3$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$t^{3} + 2 t + 1$ |
$x^{4} + 3 t$ |
$[0]$ |
$[2]$ |
| 3.12.9.2 |
$12$ |
$x^{12} + 8 x^{10} + 4 x^{9} + 33 x^{8} + 24 x^{7} - 10 x^{6} - 96 x^{5} + 163 x^{4} + 12 x^{3} - 6 x^{2} + 68 x + 172$ |
$3$ |
$4$ |
$3$ |
$9$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$4$ |
$[\ ]$ |
$[\ ]_{4}^{6}$ |
$t^{3} + 2 t + 1$ |
$x^{4} + 3$ |
$[0]$ |
$[2]$ |
| 3.12.12.1 |
$12$ |
$x^{12} - 36 x^{10} + 12 x^{9} + 540 x^{8} - 324 x^{7} - 3402 x^{6} + 3240 x^{5} + 8424 x^{4} - 10260 x^{3} + 4860 x^{2} - 972 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t^{2}\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.2 |
$12$ |
$x^{12} - 48 x^{11} + 606 x^{10} + 2856 x^{9} + 29529 x^{8} + 112428 x^{7} + 183222 x^{6} + 125172 x^{5} + 19926 x^{4} + 3024 x^{3} + 9072 x^{2} - 1620 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t + 3\right) x^{2} + \left(6 t^{3} + 6 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.3 |
$12$ |
$x^{12} + 6 x^{11} + 60 x^{10} + 210 x^{9} + 1170 x^{8} + 2322 x^{7} + 1782 x^{6} + 6048 x^{5} + 13527 x^{4} + 8370 x^{3} + 2916 x^{2} + 648 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 3 t + 6\right) x^{2} + \left(6 t^{2} + 6 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.4 |
$12$ |
$x^{12} - 24 x^{11} + 192 x^{10} + 1236 x^{9} + 2160 x^{8} + 7560 x^{7} + 29430 x^{6} + 30456 x^{5} + 6804 x^{4} - 540 x^{3} + 1296 x^{2} - 648 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$F_9$ (as 12T46) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6\right) x^{2} + \left(3 t^{3} + 3 t^{2} + 6 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.5 |
$12$ |
$x^{12} - 12 x^{11} + 132 x^{10} - 204 x^{9} + 3024 x^{8} - 432 x^{7} + 3510 x^{6} + 2268 x^{5} - 972 x^{4} + 756 x^{3} + 1620 x^{2} + 648 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$S_3 \times C_4$ (as 12T11) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t^{2} + 6\right) x^{2} + 6 x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.6 |
$12$ |
$x^{12} - 24 x^{11} + 270 x^{10} - 924 x^{9} + 1557 x^{8} + 9828 x^{7} + 8694 x^{6} + 1080 x^{5} + 1134 x^{4} + 1404 x^{3} + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_6.D_6$ (as 12T39) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t^{2} + 3\right) x^{2} + \left(6 t^{3} + 6 t^{2} + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.7 |
$12$ |
$x^{12} + 6 x^{11} + 24 x^{10} + 48 x^{9} + 576 x^{8} + 5508 x^{7} + 19710 x^{6} + 29538 x^{5} + 13608 x^{4} - 3456 x^{3} + 1458 x^{2} - 324 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^2:C_4\times S_3$ (as 12T119) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 3 t + 6\right) x^{2} + \left(6 t^{3} + 6 t^{2} + 6 t + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.8 |
$12$ |
$x^{12} + 42 x^{11} + 732 x^{10} + 6888 x^{9} + 37836 x^{8} + 101736 x^{7} + 148230 x^{6} + 129006 x^{5} + 72900 x^{4} + 28944 x^{3} + 8262 x^{2} + 1296 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^2:C_4\times S_3$ (as 12T119) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 3 t + 6\right) x^{2} + \left(6 t^{2} + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.9 |
$12$ |
$x^{12} + 6 x^{11} - 12 x^{10} - 60 x^{9} + 261 x^{8} + 540 x^{7} + 540 x^{6} + 1728 x^{5} + 2187 x^{4} - 1674 x^{3} + 1296 x^{2} - 324 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_2\times C_3^2:C_4$ (as 12T41) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t + 3\right) x^{2} + \left(6 t^{3} + 6 t^{2} + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.10 |
$12$ |
$x^{12} - 24 x^{11} + 306 x^{10} - 2004 x^{9} + 7236 x^{8} - 4374 x^{7} - 1458 x^{6} + 5832 x^{5} - 1836 x^{3} + 324 x^{2} + 486 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2}\right) x^{2} + \left(3 t + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.11 |
$12$ |
$x^{12} - 48 x^{11} + 846 x^{10} - 5820 x^{9} + 38376 x^{8} + 37098 x^{7} - 36666 x^{6} - 17928 x^{5} + 11340 x^{4} - 1188 x^{3} + 486 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t^{2} + 6 t\right) x^{2} + \left(6 t^{2} + 3 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.12 |
$12$ |
$x^{12} - 12 x^{11} + 156 x^{10} - 1104 x^{9} + 3420 x^{8} + 972 x^{7} - 1890 x^{6} + 1404 x^{5} + 1944 x^{4} + 432 x^{3} + 324 x^{2} + 324 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_2\times C_3^2:C_4$ (as 12T41) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t^{2} + 6 t\right) x^{2} + \left(3 t^{3} + 3 t^{2} + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.13 |
$12$ |
$x^{12} - 36 x^{11} + 324 x^{10} + 588 x^{9} + 9414 x^{8} + 56376 x^{7} + 114642 x^{6} + 92448 x^{5} + 23409 x^{4} + 2376 x^{3} + 3078 x^{2} - 972 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t\right) x^{2} + \left(6 t^{3} + 3 t^{2} + 6 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.14 |
$12$ |
$x^{12} + 54 x^{10} - 240 x^{9} - 1935 x^{8} + 7236 x^{7} + 45198 x^{6} + 60156 x^{5} + 16686 x^{4} - 13824 x^{3} + 5184 x^{2} - 972 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t^{2} + 6 t + 3\right) x^{2} + \left(6 t^{3} + 6 t^{2} + 6 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.15 |
$12$ |
$x^{12} - 18 x^{11} + 186 x^{10} - 798 x^{9} + 2817 x^{8} + 30456 x^{7} + 55404 x^{6} + 28404 x^{5} - 2511 x^{4} + 918 x^{3} + 2754 x^{2} - 810 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 3 t + 3\right) x^{2} + \left(6 t^{3} + 3 t^{2} + 3 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.16 |
$12$ |
$x^{12} - 18 x^{11} + 30 x^{10} + 1020 x^{9} + 3249 x^{8} + 6480 x^{7} + 21924 x^{6} + 35208 x^{5} + 7452 x^{4} - 8478 x^{3} + 5670 x^{2} - 1134 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t + 3\right) x^{2} + \left(6 t^{3} + 3 t^{2} + 3 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.17 |
$12$ |
$x^{12} + 36 x^{11} + 540 x^{10} + 3900 x^{9} + 8028 x^{8} - 44388 x^{7} + 21870 x^{6} + 7020 x^{5} + 20412 x^{4} - 8316 x^{3} + 4212 x^{2} - 972 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + \left(3 t^{3} + 6 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.18 |
$12$ |
$x^{12} - 36 x^{11} + 438 x^{10} + 120 x^{9} - 4563 x^{8} + 1188 x^{7} + 22410 x^{6} + 10692 x^{5} - 17658 x^{4} - 3780 x^{3} + 6804 x^{2} - 1296 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$F_9$ (as 12T46) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3\right) x^{2} + 6 t^{3} x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.19 |
$12$ |
$x^{12} - 12 x^{11} + 78 x^{10} - 564 x^{9} + 5913 x^{8} - 7182 x^{6} + 972 x^{5} + 7614 x^{4} + 3024 x^{3} + 1620 x^{2} + 648 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^2:C_4\times S_3$ (as 12T119) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 6 t + 3\right) x^{2} + \left(3 t^{3} + 6 t^{2} + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.20 |
$12$ |
$x^{12} + 30 x^{10} + 228 x^{9} + 1872 x^{8} + 5778 x^{7} + 15336 x^{6} + 18036 x^{5} + 12879 x^{4} + 7074 x^{3} + 3240 x^{2} + 810 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t^{2}\right) x^{2} + \left(6 t^{2} + 3 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.21 |
$12$ |
$x^{12} - 6 x^{11} + 60 x^{10} - 114 x^{9} + 2286 x^{8} + 33750 x^{7} + 101790 x^{6} + 91152 x^{5} + 24867 x^{4} + 6102 x^{3} + 5832 x^{2} - 1296 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 3 t + 6\right) x^{2} + \left(6 t^{3} + 6 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.22 |
$12$ |
$x^{12} + 36 x^{11} + 426 x^{10} + 2172 x^{9} + 14769 x^{8} + 20628 x^{7} + 31050 x^{6} + 11016 x^{5} + 7938 x^{4} + 3672 x^{3} + 972 x^{2} + 324 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$C_3^2:C_4\times S_3$ (as 12T119) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2, 3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 3\right) x^{2} + \left(6 t + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.23 |
$12$ |
$x^{12} + 6 x^{11} + 12 x^{10} + 12 x^{9} + 189 x^{8} + 108 x^{7} + 324 x^{6} + 648 x^{5} + 891 x^{4} + 918 x^{3} + 648 x^{2} + 324 x + 81$ |
$3$ |
$3$ |
$4$ |
$12$ |
$S_3 \times C_4$ (as 12T11) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t + 3\right) x^{2} + 3 x + 3$ |
$[1, 0]$ |
$[1]$ |
| 3.12.12.24 |
$12$ |
$x^{12} - 12 x^{7} - 6 x^{6} + 72 x^{2} + 72 x + 18$ |
$3$ |
$6$ |
$2$ |
$12$ |
$C_3^4:\OD_{16}$ (as 12T215) |
$4$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4, 5/4]_{4}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 t x + 3 t$ |
$[1, 0]$ |
$[1, 1]$ |
| 3.12.12.25 |
$12$ |
$x^{12} - 6 x^{7} - 6 x^{6} + 9 x^{4} + 36 x^{3} + 63 x^{2} + 54 x + 18$ |
$3$ |
$6$ |
$2$ |
$12$ |
$C_3^4:\OD_{16}$ (as 12T215) |
$4$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4, 5/4, 5/4]_{4}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{2} + \left(6 t + 3\right) x + 3 t$ |
$[1, 0]$ |
$[1, 1]$ |
| 3.12.12.26 |
$12$ |
$x^{12} - 12 x^{8} + 6 x^{7} + 6 x^{6} + 72 x^{4} - 36 x^{3} - 27 x^{2} + 18 x + 9$ |
$3$ |
$6$ |
$2$ |
$12$ |
$\SOPlus(4,2)$ (as 12T34) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 t x^{2} + 3 x + 3$ |
$[1, 0]$ |
$[1, 1]$ |
| 3.12.12.27 |
$12$ |
$x^{12} - 12 x^{7} + 6 x^{6} + 9 x^{4} + 36 x^{3} + 72 x^{2} - 36 x + 9$ |
$3$ |
$6$ |
$2$ |
$12$ |
$\PSU(3,2)$ (as 12T47) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{2} + 6 t x + 3$ |
$[1, 0]$ |
$[1, 1]$ |
| 3.12.12.28 |
$12$ |
$x^{12} + 6 x^{6} + 36 x^{4} + 36 x^{3} + 9 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$12$ |
$\SOPlus(4,2)$ (as 12T34) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{2} + \left(3 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1, 1]$ |
| 3.12.12.29 |
$12$ |
$x^{12} + 3 x + 3$ |
$3$ |
$12$ |
$1$ |
$12$ |
$F_9:C_2$ (as 12T84) |
$2$ |
$8$ |
$[9/8]$ |
$[9/8, 9/8]_{8}^{2}$ |
$t + 1$ |
$x^{12} + 3 x + 3$ |
$[1, 0]$ |
$[1, 2]$ |
| 3.12.12.30 |
$12$ |
$x^{12} + 3 x^{2} + 3 x + 6$ |
$3$ |
$12$ |
$1$ |
$12$ |
$F_9:C_2$ (as 12T84) |
$2$ |
$8$ |
$[9/8]$ |
$[9/8, 9/8]_{8}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{2} + 3 x + 6$ |
$[1, 0]$ |
$[1, 2]$ |
| 3.12.13.1 |
$12$ |
$x^{12} + 3 x^{2} + 3$ |
$3$ |
$12$ |
$1$ |
$13$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[2, 2]$ |
| 3.12.13.2 |
$12$ |
$x^{12} + 3 x^{3} + 6 x^{2} + 3$ |
$3$ |
$12$ |
$1$ |
$13$ |
$S_3^2:C_6$ (as 12T121) |
$6$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{3} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1, 2]$ |
| 3.12.13.3 |
$12$ |
$x^{12} + 3 x^{3} + 3 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$13$ |
$S_3^2:C_6$ (as 12T121) |
$6$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{6}$ |
$t + 1$ |
$x^{12} + 3 x^{3} + 3 x^{2} + 6$ |
$[2, 0]$ |
$[1, 2]$ |
| 3.12.13.4 |
$12$ |
$x^{12} + 6 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$13$ |
$\SOPlus(4,2)$ (as 12T36) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{2} + 6$ |
$[2, 0]$ |
$[2, 2]$ |
| 3.12.13.5 |
$12$ |
$x^{12} + 6 x^{2} + 3$ |
$3$ |
$12$ |
$1$ |
$13$ |
$\SOPlus(4,2)$ (as 12T35) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1, 2]$ |
| 3.12.13.6 |
$12$ |
$x^{12} + 3 x^{2} + 6$ |
$3$ |
$12$ |
$1$ |
$13$ |
$\SOPlus(4,2)$ (as 12T35) |
$2$ |
$4$ |
$[5/4]$ |
$[5/4, 5/4]_{4}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{2} + 6$ |
$[2, 0]$ |
$[1, 2]$ |
| 3.12.14.1 |
$12$ |
$x^{12} - 6 x^{8} - 6 x^{6} + 18 x^{4} + 36 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$(C_3\times C_3):C_4$ (as 12T17) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
| 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) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{3} + \left(3 t + 6\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.3 |
$12$ |
$x^{12} + 30 x^{6} + 72 x^{5} + 36 x^{4} + 36 x^{3} + 36 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$S_3 \times C_4$ (as 12T11) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{3} + \left(6 t + 6\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.12.14.4 |
$12$ |
$x^{12} - 6 x^{9} - 12 x^{8} + 24 x^{6} + 72 x^{5} + 72 x^{4} - 18 x^{3} - 36 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_2\times C_3^2:C_4$ (as 12T40) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{3} + 6 t x^{2} + 3$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.12.14.5 |
$12$ |
$x^{12} + 6 x^{6} + 36 x^{4} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$S_3^2$ (as 12T16) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.6 |
$12$ |
$x^{12} + 6 x^{8} + 15 x^{6} + 9 x^{4} + 18 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$D_6$ (as 12T3) |
$2$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.7 |
$12$ |
$x^{12} + 12 x^{9} - 6 x^{8} + 42 x^{6} - 36 x^{5} + 18 x^{4} + 36 x^{3} - 18 x^{2} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_2\times C_3^2:C_4$ (as 12T40) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{3} + 3 t x^{2} + 3$ |
$[2, 0]$ |
$[2, 1]$ |
| 3.12.14.8 |
$12$ |
$x^{12} + 42 x^{6} + 72 x^{5} + 36 x^{4} + 9$ |
$3$ |
$6$ |
$2$ |
$14$ |
$C_3\times S_3^2$ (as 12T70) |
$6$ |
$2$ |
$[3/2]$ |
$[3/2, 3/2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{3} + \left(6 t + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
| 3.12.14.9 |
$12$ |
$x^{12} - 6 x^{9} + 12 x^{6} + 18 x^{5} + 9 x^{4} + 36 x^{3} + 18 x^{2} + 18$ |
$3$ |
$6$ |
$2$ |
$14$ |
$S_3 \times C_4$ (as 12T11) |
$4$ |
$2$ |
$[3/2]$ |
$[3/2]_{2}^{4}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{3} + \left(3 t + 3\right) x^{2} + 3 t$ |
$[2, 0]$ |
$[2, 1]$ |
