| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 3.12.16.1 |
$12$ |
$x^{12} + 36 x^{10} - 186 x^{9} + 432 x^{8} - 1404 x^{7} + 1836 x^{6} - 3240 x^{5} + 7128 x^{4} + 2538 x^{3} + 33048 x^{2} + 69093$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{2} + 6 t\right) x^{2} + 9 t^{3} + 9 t^{2} + 9 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 3 t^{2} x^{2} + 9 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.11 |
$12$ |
$x^{12} - 42 x^{11} + 684 x^{10} - 4470 x^{9} + 19764 x^{8} - 11124 x^{7} + 127548 x^{6} - 2754 x^{5} + 453276 x^{4} + 9342 x^{3} + 887274 x^{2} + 714501$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t^{2} + 3 t\right) x^{2} + 18 t^{3} + 9 t^{2} + 9 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t^{2} + 6\right) x^{2} + 9 t^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.13 |
$12$ |
$x^{12} - 30 x^{11} + 252 x^{10} + 2118 x^{9} + 11448 x^{8} + 540 x^{7} + 70524 x^{6} - 12150 x^{5} + 226800 x^{4} - 11070 x^{3} + 295650 x^{2} + 128385$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t + 6\right) x^{2} + 9 t^{3} + 9 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.14 |
$12$ |
$x^{12} + 24 x^{11} + 216 x^{10} + 768 x^{9} - 432 x^{8} - 10368 x^{7} - 18414 x^{6} + 27864 x^{5} + 83592 x^{4} + 10800 x^{3} + 64800 x^{2} + 901125$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_{12}$ (as 12T1) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 6 x^{2} + 9 t^{3} + 18 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.15 |
$12$ |
$x^{12} - 36 x^{11} + 360 x^{10} - 240 x^{9} + 11880 x^{8} - 7560 x^{7} + 42498 x^{6} - 9396 x^{5} + 79056 x^{4} - 2808 x^{3} + 50544 x^{2} + 13689$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t\right) x^{2} + 9 t^{3} + 9 t^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 6 t + 3\right) x^{2} + 18 t^{3} + 18 t^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.18 |
$12$ |
$x^{12} - 474 x^{9} + 5292 x^{8} - 972 x^{7} + 66960 x^{6} + 9396 x^{5} + 274104 x^{4} + 15660 x^{3} + 432540 x^{2} + 234090$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:F_9$ (as 12T173) |
$8$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{8}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 6 t + 6\right) x^{2} + 9 t^{3} + 9 t + 12$ |
$[2, 0]$ |
$[2]$ |
| 3.12.16.19 |
$12$ |
$x^{12} - 24 x^{11} + 216 x^{10} - 1392 x^{9} + 10908 x^{8} - 6480 x^{7} + 92880 x^{6} - 7776 x^{5} + 264384 x^{4} - 8640 x^{3} + 207360 x^{2} + 51840$ |
$3$ |
$3$ |
$4$ |
$16$ |
$F_9$ (as 12T46) |
$8$ |
$1$ |
$[2]$ |
$[2, 2]^{8}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 6 t\right) x^{2} + 18 t^{3} + 12$ |
$[2, 0]$ |
$[2]$ |
| 3.12.16.2 |
$12$ |
$x^{12} - 54 x^{10} - 258 x^{9} + 2403 x^{8} - 1134 x^{7} + 27594 x^{6} - 6480 x^{5} + 134136 x^{4} - 26136 x^{3} + 351864 x^{2} + 490698$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:F_9$ (as 12T173) |
$8$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{8}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t + 3\right) x^{2} + 18 t^{3} + 18 t^{2} + 9 t + 12$ |
$[2, 0]$ |
$[2]$ |
| 3.12.16.20 |
$12$ |
$x^{12} - 54 x^{11} + 1008 x^{10} - 4902 x^{9} + 11448 x^{8} + 43632 x^{7} - 73656 x^{6} - 51354 x^{5} + 538812 x^{4} + 13230 x^{3} - 216270 x^{2} + 40905$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t\right) x^{2} + 9 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t + 3\right) x^{2} + 18 t^{3} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.22 |
$12$ |
$x^{12} + 12 x^{11} + 72 x^{10} + 192 x^{9} + 324 x^{8} + 432 x^{7} + 2808 x^{6} - 3240 x^{5} + 12312 x^{4} - 12528 x^{3} + 121824 x^{2} + 517428$ |
$3$ |
$3$ |
$4$ |
$16$ |
$(C_3\times C_3):C_4$ (as 12T17) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 6\right) x^{2} + 9 t^{3} + 9 t^{2} + 18 t + 12$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.23 |
$12$ |
$x^{12} + 24 x^{11} + 306 x^{10} + 2244 x^{9} + 8397 x^{8} + 12852 x^{7} + 48006 x^{6} + 31752 x^{5} + 134946 x^{4} + 37044 x^{3} + 222264 x^{2} + 194481$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 6 t + 3\right) x^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.24 |
$12$ |
$x^{12} - 24 x^{11} + 216 x^{10} + 930 x^{9} + 108 x^{8} + 4536 x^{7} + 23868 x^{6} - 23976 x^{5} + 69984 x^{4} + 25380 x^{3} - 210600 x^{2} + 146610$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$12$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{12}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6\right) x^{2} + 9 t^{2} + 9 t + 12$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.25 |
$12$ |
$x^{12} + 24 x^{11} + 216 x^{10} + 804 x^{9} + 216 x^{8} - 6480 x^{7} - 11610 x^{6} + 16200 x^{5} + 48600 x^{4} + 33156 x^{3} + 198936 x^{2} + 190593$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_{12}$ (as 12T1) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 6 x^{2} + 18 t^{3} + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.26 |
$12$ |
$x^{12} - 18 x^{11} + 144 x^{10} - 690 x^{9} + 2970 x^{8} - 6588 x^{7} + 33588 x^{6} - 23004 x^{5} + 185976 x^{4} - 26136 x^{3} + 486972 x^{2} + 490698$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:F_9$ (as 12T173) |
$8$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{8}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 3 t\right) x^{2} + 18 t^{3} + 18 t^{2} + 9 t + 12$ |
$[2, 0]$ |
$[2]$ |
| 3.12.16.27 |
$12$ |
$x^{12} + 24 x^{11} + 198 x^{10} + 624 x^{9} + 837 x^{8} + 1512 x^{7} + 12690 x^{6} + 13608 x^{5} + 49410 x^{4} - 22248 x^{3} - 219024 x^{2} + 185733$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^3:C_4$ (as 12T72) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{2} + 3\right) x^{2} + 9 t^{3} + 18 t^{2} + 18 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.28 |
$12$ |
$x^{12} - 36 x^{11} + 360 x^{10} - 186 x^{9} + 10368 x^{8} - 1728 x^{7} + 50436 x^{6} - 9720 x^{5} + 26568 x^{4} + 5454 x^{3} - 76788 x^{2} + 25353$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t\right) x^{2} + 9 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.29 |
$12$ |
$x^{12} - 48 x^{11} + 666 x^{10} + 1146 x^{9} + 27891 x^{8} - 12690 x^{7} + 138726 x^{6} - 14580 x^{5} - 61560 x^{4} + 32670 x^{3} - 554850 x^{2} + 463725$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:F_9$ (as 12T173) |
$8$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{8}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t + 3\right) x^{2} + 18 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[2]$ |
| 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) |
$12$ |
$1$ |
$[2]$ |
$[2, 2]^{12}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 3\right) x^{2} + 18 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.30 |
$12$ |
$x^{12} + 18 x^{11} + 132 x^{10} + 590 x^{9} + 2211 x^{8} + 7308 x^{7} + 19596 x^{6} + 44190 x^{5} + 77448 x^{4} + 116568 x^{3} + 219150 x^{2} + 280620 x + 434681$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3 : C_4$ (as 12T5) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 3 x^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.31 |
$12$ |
$x^{12} + 30 x^{11} + 360 x^{10} + 2226 x^{9} + 7641 x^{8} - 4320 x^{7} - 24408 x^{6} - 21060 x^{5} - 255312 x^{4} - 22248 x^{3} + 454248 x^{2} + 2375892$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:F_9$ (as 12T173) |
$8$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{8}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 3 t + 3\right) x^{2} + 18 t^{3} + 9 t^{2} + 18 t + 12$ |
$[2, 0]$ |
$[2]$ |
| 3.12.16.32 |
$12$ |
$x^{12} + 18 x^{11} + 144 x^{10} + 822 x^{9} + 4482 x^{8} + 4104 x^{7} + 9936 x^{6} - 1296 x^{5} - 79380 x^{4} - 26136 x^{3} - 40824 x^{2} + 490698$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 3 t\right) x^{2} + 18 t^{3} + 18 t^{2} + 9 t + 12$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.33 |
$12$ |
$x^{12} + 6 x^{11} + 72 x^{10} + 308 x^{9} + 1476 x^{8} + 4692 x^{7} + 6054 x^{6} + 5154 x^{5} + 14988 x^{4} + 27588 x^{3} + 20238 x^{2} + 2280 x + 1145$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.34 |
$12$ |
$x^{12} - 60 x^{11} + 1152 x^{10} - 4308 x^{9} + 33480 x^{8} + 432 x^{7} + 96120 x^{6} - 4536 x^{5} + 95904 x^{4} + 1080 x^{3} + 12960 x^{2} + 8100$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:F_9$ (as 12T173) |
$8$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{8}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t\right) x^{2} + 9 t^{3} + 9 t^{2} + 12$ |
$[2, 0]$ |
$[2]$ |
| 3.12.16.35 |
$12$ |
$x^{12} + 18 x^{10} - 60 x^{9} + 405 x^{8} - 540 x^{7} + 3942 x^{6} - 7776 x^{5} + 59454 x^{4} + 13716 x^{3} + 568620 x^{2} + 2365929$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 3\right) x^{2} + 18 t^{3} + 9 t^{2} + 18 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.36 |
$12$ |
$x^{12} + 12 x^{11} - 546 x^{9} - 324 x^{8} - 4536 x^{7} + 57240 x^{6} + 72576 x^{5} + 587088 x^{4} + 20520 x^{3} + 844992 x^{2} + 605394$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$12$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{12}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t + 6\right) x^{2} + 18 t^{3} + 9 t + 12$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.37 |
$12$ |
$x^{12} - 6 x^{11} + 60 x^{10} - 10 x^{9} + 603 x^{8} + 3924 x^{7} + 16740 x^{6} + 36078 x^{5} + 108120 x^{4} + 201600 x^{3} + 381102 x^{2} + 225588 x + 200729$ |
$3$ |
$3$ |
$4$ |
$16$ |
$(C_3\times C_3):C_4$ (as 12T17) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 3\right) x^{2} + 18 t^{3} + 18 t^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.38 |
$12$ |
$x^{12} + 12 x^{11} + 54 x^{10} + 174 x^{9} + 675 x^{8} + 1782 x^{7} + 3618 x^{6} + 11016 x^{5} + 16524 x^{4} + 32670 x^{3} + 98010 x^{2} + 463725$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$12$ |
$1$ |
$[2]$ |
$[2]^{12}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 3 x^{2} + 18 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.39 |
$12$ |
$x^{12} + 18 x^{10} + 12 x^{9} + 189 x^{8} + 108 x^{7} + 1350 x^{6} - 1296 x^{5} + 3078 x^{4} - 3780 x^{3} - 4860 x^{2} + 11745$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$4$ |
$1$ |
$[2]$ |
$[2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 3\right) x^{2} + 9 t^{2} + 18 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.4 |
$12$ |
$x^{12} + 6 x^{11} + 36 x^{10} + 12 x^{9} + 1188 x^{8} + 864 x^{7} + 10422 x^{6} + 4050 x^{5} + 48924 x^{4} + 3996 x^{3} + 113886 x^{2} + 110889$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$12$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{12}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 3 t + 6\right) x^{2} + 18 t^{3} + 18 t^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.40 |
$12$ |
$x^{12} + 24 x^{11} + 216 x^{10} + 840 x^{9} + 864 x^{8} - 2592 x^{7} - 4482 x^{6} + 8424 x^{5} + 25272 x^{4} + 4968 x^{3} + 29808 x^{2} + 139077$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_{12}$ (as 12T1) |
$4$ |
$1$ |
$[2]$ |
$[2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 6 x^{2} + 18 t^{3} + 9 t^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.41 |
$12$ |
$x^{12} + 18 x^{11} + 144 x^{10} + 876 x^{9} + 5292 x^{8} + 6696 x^{7} + 25326 x^{6} + 5994 x^{5} + 36288 x^{4} - 3780 x^{3} - 21870 x^{2} + 11745$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 3 t\right) x^{2} + 9 t^{2} + 18 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.42 |
$12$ |
$x^{12} - 42 x^{11} + 684 x^{10} - 4578 x^{9} + 22896 x^{8} - 38340 x^{7} + 215028 x^{6} - 103518 x^{5} + 835272 x^{4} - 83970 x^{3} + 1405350 x^{2} + 842805$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t^{2} + 3 t\right) x^{2} + 18 t^{3} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.43 |
$12$ |
$x^{12} + 12 x^{11} + 90 x^{10} + 120 x^{9} + 513 x^{8} + 2484 x^{7} + 1350 x^{6} + 6156 x^{5} + 18306 x^{4} + 5940 x^{3} + 32400 x^{2} + 70065$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{2} + 6 t + 3\right) x^{2} + 9 t^{3} + 18 t^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.44 |
$12$ |
$x^{12} + 24 x^{11} + 144 x^{10} - 60 x^{9} + 4320 x^{8} + 3456 x^{7} + 1836 x^{6} - 49248 x^{4} - 16416 x^{3} + 25920 x^{2} + 175284$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$12$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{12}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 6 t^{2} x^{2} + 18 t^{3} + 9 t^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
| 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) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t^{2} + 6\right) x^{2} + 9 t^{3} + 18 t^{2} + 18 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.46 |
$12$ |
$x^{12} - 24 x^{11} + 216 x^{10} + 804 x^{9} + 1944 x^{8} + 11664 x^{7} + 33912 x^{6} + 37584 x^{5} + 295488 x^{4} + 32184 x^{3} + 981072 x^{2} + 1122984$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^3:C_4$ (as 12T72) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6\right) x^{2} + 9 t^{3} + 18 t + 12$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.47 |
$12$ |
$x^{12} + 3 x^{5} + 3$ |
$3$ |
$12$ |
$1$ |
$16$ |
$F_9:C_2$ (as 12T84) |
$2$ |
$8$ |
$[13/8]$ |
$[13/8, 13/8]_{8}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{5} + 3$ |
$[5, 0]$ |
$[1, 2]$ |
| 3.12.16.48 |
$12$ |
$x^{12} + 6 x^{7} + 3 x^{6} + 3 x^{5} + 6$ |
$3$ |
$12$ |
$1$ |
$16$ |
$F_9:C_2$ (as 12T84) |
$2$ |
$8$ |
$[13/8]$ |
$[13/8, 13/8]_{8}^{2}$ |
$t + 1$ |
$x^{12} + 6 x^{7} + 3 x^{6} + 3 x^{5} + 6$ |
$[5, 0]$ |
$[1, 2]$ |
| 3.12.16.49 |
$12$ |
$x^{12} + 3 x^{8} + 3 x^{7} + 3 x^{5} + 3 x^{3} + 6$ |
$3$ |
$12$ |
$1$ |
$16$ |
$C_3^4:\SD_{16}$ (as 12T212) |
$2$ |
$8$ |
$[13/8]$ |
$[9/8, 9/8, 13/8, 13/8]_{8}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{8} + 3 x^{7} + 3 x^{5} + 3 x^{3} + 6$ |
$[5, 0]$ |
$[1, 2]$ |
| 3.12.16.5 |
$12$ |
$x^{12} - 12 x^{11} + 144 x^{10} - 1140 x^{9} + 4104 x^{8} - 13392 x^{7} + 75546 x^{6} - 35316 x^{5} + 588384 x^{4} + 13716 x^{3} + 1828008 x^{2} + 2365929$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t^{2} + 6 t\right) x^{2} + 18 t^{3} + 9 t^{2} + 18 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.50 |
$12$ |
$x^{12} + 3 x^{6} + 3 x^{5} + 6$ |
$3$ |
$12$ |
$1$ |
$16$ |
$C_3^4:\SD_{16}$ (as 12T212) |
$2$ |
$8$ |
$[13/8]$ |
$[9/8, 9/8, 13/8, 13/8]_{8}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{6} + 3 x^{5} + 6$ |
$[5, 0]$ |
$[1, 2]$ |
| 3.12.16.51 |
$12$ |
$x^{12} + 3 x^{8} + 6 x^{6} + 3 x^{5} + 3$ |
$3$ |
$12$ |
$1$ |
$16$ |
$C_3^4:\SD_{16}$ (as 12T212) |
$2$ |
$8$ |
$[13/8]$ |
$[9/8, 9/8, 13/8, 13/8]_{8}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{8} + 6 x^{6} + 3 x^{5} + 3$ |
$[5, 0]$ |
$[1, 2]$ |
| 3.12.16.52 |
$12$ |
$x^{12} + 3 x^{8} + 3 x^{6} + 3 x^{5} + 3$ |
$3$ |
$12$ |
$1$ |
$16$ |
$C_3^4:\SD_{16}$ (as 12T212) |
$2$ |
$8$ |
$[13/8]$ |
$[9/8, 9/8, 13/8, 13/8]_{8}^{2}$ |
$t + 1$ |
$x^{12} + 3 x^{8} + 3 x^{6} + 3 x^{5} + 3$ |
$[5, 0]$ |
$[1, 2]$ |
| 3.12.16.6 |
$12$ |
$x^{12} - 30 x^{11} + 432 x^{10} - 3282 x^{9} + 15012 x^{8} - 14580 x^{7} + 93204 x^{6} - 21870 x^{5} + 238140 x^{4} - 11070 x^{3} + 281070 x^{2} + 128385$ |
$3$ |
$3$ |
$4$ |
$16$ |
$F_9$ (as 12T46) |
$8$ |
$1$ |
$[2]$ |
$[2, 2]^{8}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 3 t\right) x^{2} + 9 t^{3} + 9 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[2]$ |
| 3.12.16.7 |
$12$ |
$x^{12} - 18 x^{11} + 72 x^{10} + 444 x^{9} + 2619 x^{8} + 4806 x^{7} + 29862 x^{6} + 15228 x^{5} + 140616 x^{4} + 15660 x^{3} + 296460 x^{2} + 234090$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3^2:F_9$ (as 12T173) |
$8$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{8}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t + 3\right) x^{2} + 9 t^{3} + 9 t + 12$ |
$[2, 0]$ |
$[2]$ |
