| 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) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{2} + 6 t\right) x^{2} + 9 t^{3} + 9 t^{2} + 9 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.11 |
$12$ |
$x^{12} - 42 x^{11} + 684 x^{10} - 4470 x^{9} + 19764 x^{8} - 11124 x^{7} + 127548 x^{6} - 2754 x^{5} + 453276 x^{4} + 9342 x^{3} + 887274 x^{2} + 714501$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t^{2} + 3 t\right) x^{2} + 18 t^{3} + 9 t^{2} + 9 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.13 |
$12$ |
$x^{12} - 30 x^{11} + 252 x^{10} + 2118 x^{9} + 11448 x^{8} + 540 x^{7} + 70524 x^{6} - 12150 x^{5} + 226800 x^{4} - 11070 x^{3} + 295650 x^{2} + 128385$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t + 6\right) x^{2} + 9 t^{3} + 9 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.15 |
$12$ |
$x^{12} - 36 x^{11} + 360 x^{10} - 240 x^{9} + 11880 x^{8} - 7560 x^{7} + 42498 x^{6} - 9396 x^{5} + 79056 x^{4} - 2808 x^{3} + 50544 x^{2} + 13689$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t\right) x^{2} + 9 t^{3} + 9 t^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.20 |
$12$ |
$x^{12} - 54 x^{11} + 1008 x^{10} - 4902 x^{9} + 11448 x^{8} + 43632 x^{7} - 73656 x^{6} - 51354 x^{5} + 538812 x^{4} + 13230 x^{3} - 216270 x^{2} + 40905$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t\right) x^{2} + 9 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.23 |
$12$ |
$x^{12} + 24 x^{11} + 306 x^{10} + 2244 x^{9} + 8397 x^{8} + 12852 x^{7} + 48006 x^{6} + 31752 x^{5} + 134946 x^{4} + 37044 x^{3} + 222264 x^{2} + 194481$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (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) |
$12$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{12}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6\right) x^{2} + 9 t^{2} + 9 t + 12$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.28 |
$12$ |
$x^{12} - 36 x^{11} + 360 x^{10} - 186 x^{9} + 10368 x^{8} - 1728 x^{7} + 50436 x^{6} - 9720 x^{5} + 26568 x^{4} + 5454 x^{3} - 76788 x^{2} + 25353$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t\right) x^{2} + 9 t^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.32 |
$12$ |
$x^{12} + 18 x^{11} + 144 x^{10} + 822 x^{9} + 4482 x^{8} + 4104 x^{7} + 9936 x^{6} - 1296 x^{5} - 79380 x^{4} - 26136 x^{3} - 40824 x^{2} + 490698$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 3 t\right) x^{2} + 18 t^{3} + 18 t^{2} + 9 t + 12$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.36 |
$12$ |
$x^{12} + 12 x^{11} - 546 x^{9} - 324 x^{8} - 4536 x^{7} + 57240 x^{6} + 72576 x^{5} + 587088 x^{4} + 20520 x^{3} + 844992 x^{2} + 605394$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$12$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{12}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t + 6\right) x^{2} + 18 t^{3} + 9 t + 12$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.4 |
$12$ |
$x^{12} + 6 x^{11} + 36 x^{10} + 12 x^{9} + 1188 x^{8} + 864 x^{7} + 10422 x^{6} + 4050 x^{5} + 48924 x^{4} + 3996 x^{3} + 113886 x^{2} + 110889$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$12$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{12}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 3 t + 6\right) x^{2} + 18 t^{3} + 18 t^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.41 |
$12$ |
$x^{12} + 18 x^{11} + 144 x^{10} + 876 x^{9} + 5292 x^{8} + 6696 x^{7} + 25326 x^{6} + 5994 x^{5} + 36288 x^{4} - 3780 x^{3} - 21870 x^{2} + 11745$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (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) |
$12$ |
$1$ |
$[2]$ |
$[2, 2, 2]^{12}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 6 t^{2} x^{2} + 18 t^{3} + 9 t^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
| 3.12.16.5 |
$12$ |
$x^{12} - 12 x^{11} + 144 x^{10} - 1140 x^{9} + 4104 x^{8} - 13392 x^{7} + 75546 x^{6} - 35316 x^{5} + 588384 x^{4} + 13716 x^{3} + 1828008 x^{2} + 2365929$ |
$3$ |
$3$ |
$4$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2]^{4}$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t^{2} + 6 t\right) x^{2} + 18 t^{3} + 9 t^{2} + 18 t + 21$ |
$[2, 0]$ |
$[1]$ |
| 3.12.18.13 |
$12$ |
$x^{12} + 6 x^{11} - 3 x^{10} - 30 x^{9} + 90 x^{8} - 36 x^{7} + 21 x^{6} + 36 x^{5} + 72 x^{4} + 36 x^{3} + 180$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + 6 t x^{4} + 3 x^{3} + 12 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.14 |
$12$ |
$x^{12} - 6 x^{11} + 6 x^{10} + 72 x^{9} + 72 x^{8} + 30 x^{6} - 72 x^{5} - 144 x^{4} + 234$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{5} + 6 t x^{4} + 3 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.26 |
$12$ |
$x^{12} + 12 x^{11} + 30 x^{10} - 48 x^{9} - 54 x^{8} + 72 x^{7} + 48 x^{6} - 144 x^{5} + 144 x^{4} + 288 x^{3} + 288$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + 3 t x^{4} + 6 t x^{3} + 12 t$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.29 |
$12$ |
$x^{12} - 12 x^{10} - 6 x^{9} + 72 x^{8} + 108 x^{7} + 57 x^{6} + 72 x^{4} + 108 x^{3} + 180$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 t x^{4} + \left(6 t + 3\right) x^{3} + 12 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.32 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} - 18 x^{9} + 45 x^{8} + 36 x^{7} + 3 x^{6} - 18 x^{5} + 54 x^{4} + 18 x^{3} + 18$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$6$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + \left(6 t + 3\right) x^{4} + \left(3 t + 3\right) x^{3} + 3 t$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.33 |
$12$ |
$x^{12} + 6 x^{11} + 3 x^{10} - 30 x^{9} - 18 x^{8} + 72 x^{7} + 66 x^{6} - 18 x^{5} + 36 x^{4} + 72 x^{3} + 18$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{5} + 3 t x^{4} + 6 t x^{3} + 3 t$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.38 |
$12$ |
$x^{12} - 12 x^{11} + 66 x^{10} + 108 x^{9} + 81 x^{8} + 36 x^{7} - 33 x^{6} + 504 x^{5} + 378 x^{4} + 126 x^{3} + 882$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$6$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 t x^{5} + \left(6 t + 3\right) x^{4} + \left(3 t + 3\right) x^{3} + 21 t$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.40 |
$12$ |
$x^{12} + 3 x^{10} + 18 x^{9} + 54 x^{8} + 36 x^{7} - 6 x^{6} + 126 x^{5} + 252 x^{4} + 252 x^{3} + 882$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(3 t + 3\right) x^{5} + 3 t x^{4} + \left(6 t + 6\right) x^{3} + 21 t$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.47 |
$12$ |
$x^{12} - 6 x^{11} + 39 x^{10} + 102 x^{9} + 9 x^{8} - 36 x^{7} + 30 x^{6} + 54 x^{5} + 54 x^{4} - 36 x^{3} + 18$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$6$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{5} + \left(6 t + 3\right) x^{4} + 6 x^{3} + 3 t$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.5 |
$12$ |
$x^{12} - 6 x^{10} - 12 x^{9} + 18 x^{8} + 72 x^{7} + 66 x^{6} + 144 x^{4} + 288 x^{3} + 450$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{4} + 6 t x^{3} + 21 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.52 |
$12$ |
$x^{12} - 6 x^{11} + 6 x^{10} + 78 x^{9} + 54 x^{8} - 36 x^{7} + 21 x^{6} - 18 x^{5} - 36 x^{4} + 36 x^{3} + 45$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 t x^{5} + 6 t x^{4} + 3 x^{3} + 3 t + 9$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.53 |
$12$ |
$x^{12} - 6 x^{11} + 33 x^{10} + 108 x^{9} + 72 x^{8} + 12 x^{6} - 36 x^{4} + 45$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 3\right) x^{5} + 6 t x^{4} + 3 t + 9$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.55 |
$12$ |
$x^{12} - 12 x^{10} - 6 x^{9} + 72 x^{8} + 72 x^{7} - 6 x^{6} + 396 x^{4} + 198 x^{3} + 585$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 t x^{4} + 3 t x^{3} + 21 t + 9$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.65 |
$12$ |
$x^{12} + 24 x^{10} + 72 x^{9} + 72 x^{8} - 24 x^{6} + 144 x^{5} + 288 x^{4} + 288$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{5} + 6 t x^{4} + 12 t$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.67 |
$12$ |
$x^{12} - 12 x^{11} + 60 x^{10} + 150 x^{9} + 72 x^{8} + 30 x^{6} + 72 x^{5} + 72 x^{4} + 108 x^{3} + 180$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$2$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2, 2]_{2}^{2}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 t x^{5} + 6 t x^{4} + \left(3 t + 6\right) x^{3} + 12 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
| 3.12.18.81 |
$12$ |
$x^{12} + 12 x^{11} + 30 x^{10} - 48 x^{9} - 27 x^{8} + 108 x^{7} + 66 x^{6} - 36 x^{5} + 270 x^{4} + 288 x^{3} + 450$ |
$3$ |
$6$ |
$2$ |
$18$ |
$C_3\wr C_4$ (as 12T131) |
$6$ |
$2$ |
$[2]$ |
$[3/2, 3/2, 2]_{2}^{6}$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 6 x^{5} + \left(6 t + 3\right) x^{4} + 6 t x^{3} + 21 t + 18$ |
$[4, 0]$ |
$[1, 1]$ |
