| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.12.1 |
$12$ |
$x^{12} + 16 x^{11} + 100 x^{10} + 184 x^{9} + 44 x^{8} - 1472 x^{7} - 2336 x^{6} - 1600 x^{5} + 18032 x^{4} + 37504 x^{3} + 66880 x^{2} + 40064 x + 13120$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2\right) x + 4 t^{4} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.14 |
$12$ |
$x^{12} - 6 x^{11} + 36 x^{10} - 164 x^{9} + 660 x^{8} - 2352 x^{7} + 6720 x^{6} - 15584 x^{5} + 28656 x^{4} - 41056 x^{3} + 48320 x^{2} - 37696 x + 22720$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3}\right) x + 4 t^{3} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.15 |
$12$ |
$x^{12} - 4 x^{11} + 44 x^{10} - 152 x^{9} + 692 x^{8} - 1952 x^{7} + 6624 x^{6} - 12224 x^{5} + 33776 x^{4} - 54976 x^{3} + 73920 x^{2} - 129664 x + 96448$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{2}\right) x + 4 t^{3} + 4 t^{2} + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.16 |
$12$ |
$x^{12} - 6 x^{11} + 16 x^{10} - 12 x^{9} - 68 x^{8} + 16 x^{7} + 832 x^{6} - 4320 x^{5} + 11632 x^{4} - 6240 x^{3} + 13568 x^{2} + 9536 x + 1600$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3}\right) x + 4 t^{5} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.21 |
$12$ |
$x^{12} + 16 x^{11} + 88 x^{10} + 24 x^{9} - 1308 x^{8} - 4288 x^{7} - 736 x^{6} + 26176 x^{5} + 68592 x^{4} + 77696 x^{3} + 42752 x^{2} + 13440 x + 4544$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2\right) x + 4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.22 |
$12$ |
$x^{12} + 10 x^{11} - 16 x^{10} - 316 x^{9} - 364 x^{8} + 1040 x^{7} + 7648 x^{6} + 17632 x^{5} + 25008 x^{4} + 17056 x^{3} + 6016 x^{2} + 1344 x + 4544$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2\right) x + 4 t^{5} + 4 t^{3} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.3 |
$12$ |
$x^{12} - 4 x^{11} + 52 x^{10} - 128 x^{9} + 532 x^{8} - 1184 x^{7} + 6080 x^{6} - 2304 x^{5} + 36144 x^{4} - 10688 x^{3} + 86208 x^{2} - 38656 x + 107968$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{2}\right) x + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 6$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.7 |
$12$ |
$x^{12} + 2 x^{11} + 8 x^{10} + 108 x^{9} + 452 x^{8} + 1328 x^{7} + 5952 x^{6} + 25760 x^{5} + 72688 x^{4} + 129184 x^{3} + 143232 x^{2} + 92096 x + 26560$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t^{2} + 2\right) x + 4 t^{3} + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.18.1 |
$12$ |
$x^{12} - 8 x^{11} + 16 x^{10} + 64 x^{9} - 620 x^{8} - 7680 x^{7} + 12224 x^{6} + 203648 x^{5} + 795312 x^{4} + 1213568 x^{3} + 1855488 x^{2} + 2545152 x + 1772480$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 4 t^{2} x + 4 t^{5} + 12 t^{3} + 12 t^{2} + 12 t + 10$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.14 |
$12$ |
$x^{12} - 12 x^{11} + 132 x^{10} - 1224 x^{9} + 9404 x^{8} - 20960 x^{7} + 226016 x^{6} + 258496 x^{5} + 3156720 x^{4} + 3669056 x^{3} + 31019072 x^{2} + 1809792 x + 1196096$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t\right) x + 8 t^{5} + 8 t^{4} + 8 t^{2} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.16 |
$12$ |
$x^{12} + 4 x^{11} + 92 x^{10} + 632 x^{9} + 3244 x^{8} + 12448 x^{7} + 29344 x^{6} + 151488 x^{5} + 499312 x^{4} + 678208 x^{3} + 3019712 x^{2} + 5071232 x + 4682560$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4\right) x + 8 t^{5} + 8 t^{4} + 8 t^{3} + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.17 |
$12$ |
$x^{12} + 12 x^{11} + 124 x^{10} + 328 x^{9} + 8076 x^{8} + 56800 x^{7} + 333472 x^{6} + 1195584 x^{5} + 3358576 x^{4} + 6370240 x^{3} + 9140672 x^{2} + 7707264 x + 4247872$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 8 t^{4} + 8 t^{3} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.19 |
$12$ |
$x^{12} - 4 x^{11} + 12 x^{10} - 1464 x^{9} + 8348 x^{8} + 3680 x^{7} + 152224 x^{6} + 371008 x^{5} + 1270256 x^{4} + 2534080 x^{3} + 4709568 x^{2} + 4877952 x + 2395712$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3}\right) x + 4 t^{5} + 8 t^{4} + 8 t^{3} + 4 t^{2} + 4 t + 10$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.21 |
$12$ |
$x^{12} - 12 x^{11} + 76 x^{10} - 1064 x^{9} + 9132 x^{8} - 1248 x^{7} + 100384 x^{6} + 81088 x^{5} + 857712 x^{4} + 1515584 x^{3} + 3413696 x^{2} + 3749760 x + 4682560$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t\right) x + 8 t^{5} + 8 t^{4} + 8 t^{3} + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.3 |
$12$ |
$x^{12} + 4 x^{11} + 148 x^{10} + 600 x^{9} + 6524 x^{8} + 24224 x^{7} + 103520 x^{6} + 191168 x^{5} + 1586928 x^{4} + 6269248 x^{3} + 19370304 x^{2} + 18016128 x + 9253952$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4\right) x + 8 t^{5} + 8 t^{4} + 8 t^{2} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.9 |
$12$ |
$x^{12} - 20 x^{11} + 276 x^{10} - 2232 x^{9} + 13628 x^{8} - 58912 x^{7} + 219232 x^{6} - 653248 x^{5} + 1677552 x^{4} - 3291712 x^{3} + 6175040 x^{2} - 6483328 x + 8417344$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2}\right) x + 8 t^{5} + 8 t^{4} + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.12.24.112 |
$12$ |
$x^{12} + 12 x^{11} + 58 x^{10} + 148 x^{9} + 210 x^{8} + 160 x^{7} + 256 x^{6} + 928 x^{5} + 2436 x^{4} + 3440 x^{3} + 2920 x^{2} + 912 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 6\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.121 |
$12$ |
$x^{12} + 4 x^{11} + 70 x^{10} + 212 x^{9} + 206 x^{8} + 752 x^{7} + 688 x^{6} + 896 x^{5} + 1300 x^{4} + 944 x^{3} + 600 x^{2} + 976 x + 88$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + 2 x^{2} + \left(4 t^{2} + 4\right) x + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.127 |
$12$ |
$x^{12} + 12 x^{11} + 58 x^{10} + 144 x^{9} + 242 x^{8} + 368 x^{7} + 688 x^{6} + 1120 x^{5} + 1956 x^{4} + 1104 x^{3} + 1096 x^{2} - 704 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 4 t + 6\right) x^{2} + 4 t x + 8 t^{2} + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.128 |
$12$ |
$x^{12} + 26 x^{10} - 12 x^{9} + 182 x^{8} + 384 x^{7} + 448 x^{6} + 1040 x^{5} + 1252 x^{4} + 1056 x^{3} + 1128 x^{2} + 624 x + 344$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t^{2} + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 4 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.163 |
$12$ |
$x^{12} + 12 x^{11} + 46 x^{10} + 52 x^{9} + 58 x^{8} + 320 x^{7} + 288 x^{6} + 944 x^{5} + 724 x^{4} + 1168 x^{3} + 536 x^{2} + 432 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 4 t + 2\right) x^{2} + \left(4 t^{2} + 4\right) x + 4 t^{2} + 4 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.179 |
$12$ |
$x^{12} - 2 x^{10} - 2 x^{8} + 48 x^{7} + 112 x^{6} + 160 x^{5} + 580 x^{4} + 224 x^{3} + 984 x^{2} + 320 x + 888$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 2\right) x^{2} + 4 t x + 8 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.215 |
$12$ |
$x^{12} + 12 x^{11} + 82 x^{10} + 232 x^{9} + 430 x^{8} + 656 x^{7} + 960 x^{6} + 1200 x^{5} + 964 x^{4} + 880 x^{3} + 1288 x^{2} + 896 x + 888$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 6\right) x^{2} + 4 t^{2} x + 8 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.222 |
$12$ |
$x^{12} - 2 x^{10} + 4 x^{9} + 78 x^{8} + 32 x^{7} + 240 x^{6} + 496 x^{5} + 1860 x^{4} + 2336 x^{3} + 4632 x^{2} + 2672 x + 3384$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 2\right) x^{2} + \left(4 t^{2} + 4\right) x + 12 t^{2} + 4 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.224 |
$12$ |
$x^{12} + 6 x^{10} + 30 x^{8} + 32 x^{7} + 96 x^{6} - 32 x^{5} + 116 x^{4} + 320 x^{3} + 376 x^{2} + 320 x + 536$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 2\right) x^{2} + 4 t x + 8 t^{2} + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.240 |
$12$ |
$x^{12} + 4 x^{11} + 6 x^{10} + 120 x^{9} + 122 x^{8} + 368 x^{7} + 224 x^{6} + 448 x^{5} + 532 x^{4} + 240 x^{3} + 248 x^{2} + 224 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4\right) x^{3} + \left(4 t + 2\right) x^{2} + 4 t^{2} x + 4 t^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.256 |
$12$ |
$x^{12} - 8 x^{11} + 22 x^{10} + 72 x^{9} + 86 x^{8} + 224 x^{7} + 432 x^{6} + 192 x^{5} + 708 x^{4} + 288 x^{3} + 696 x^{2} + 480 x + 344$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(4 t + 2\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 4 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.28 |
$12$ |
$x^{12} + 10 x^{10} + 12 x^{9} + 90 x^{8} + 160 x^{7} + 592 x^{6} + 688 x^{5} + 1428 x^{4} + 736 x^{3} + 552 x^{2} + 16 x - 248$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 6\right) x^{2} + \left(4 t + 4\right) x + 4 t^{2} + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.36 |
$12$ |
$x^{12} + 12 x^{11} + 66 x^{10} + 212 x^{9} + 470 x^{8} + 896 x^{7} + 1712 x^{6} + 2944 x^{5} + 3860 x^{4} + 4592 x^{3} + 5512 x^{2} + 3984 x + 3576$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t + 6\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 8 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.47 |
$12$ |
$x^{12} + 34 x^{10} - 20 x^{9} + 66 x^{8} + 80 x^{7} + 192 x^{6} + 384 x^{5} + 404 x^{4} + 224 x^{3} + 104 x^{2} - 16 x - 24$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t + 6\right) x^{2} + \left(4 t + 4\right) x + 4 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.62 |
$12$ |
$x^{12} + 12 x^{11} + 66 x^{10} + 200 x^{9} + 338 x^{8} + 256 x^{7} + 16 x^{6} + 20 x^{4} - 464 x^{3} + 520 x^{2} + 1888 x + 1768$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + 6 x^{2} + 4 t^{2} x + 12 t^{2} + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.91 |
$12$ |
$x^{12} + 18 x^{10} + 90 x^{8} + 16 x^{6} + 240 x^{5} + 84 x^{4} + 1376 x^{3} + 3272 x^{2} - 1824 x - 376$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 6 x^{2} + 4 t x + 12 t^{2} + 12 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.113 |
$12$ |
$x^{12} + 12 x^{11} + 54 x^{10} + 120 x^{9} + 358 x^{8} + 1408 x^{7} + 976 x^{6} + 4096 x^{5} + 1892 x^{4} + 10800 x^{3} + 1848 x^{2} + 6752 x + 3032$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(12 t + 2\right) x^{2} + \left(8 t^{2} + 8\right) x + 12 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.114 |
$12$ |
$x^{12} + 6 x^{10} + 24 x^{9} - 26 x^{8} + 96 x^{7} + 2400 x^{6} - 128 x^{5} + 4964 x^{4} + 4032 x^{3} + 5528 x^{2} + 2528 x - 104$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(12 t^{2} + 10\right) x^{2} + 8 x + 4 t^{2} + 12 t + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.124 |
$12$ |
$x^{12} + 12 x^{11} + 74 x^{10} + 208 x^{9} + 530 x^{8} + 1008 x^{7} + 2032 x^{6} + 3328 x^{5} + 3540 x^{4} + 3408 x^{3} + 4008 x^{2} + 1408 x + 1384$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t^{2} + 4 t + 6\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 4 t^{2} + 8 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.128 |
$12$ |
$x^{12} + 12 x^{11} + 82 x^{10} + 384 x^{9} + 1306 x^{8} + 2832 x^{7} + 5168 x^{6} + 3584 x^{5} + 2868 x^{4} + 784 x^{3} + 776 x^{2} + 64 x + 72$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t^{2} + 4 t + 14\right) x^{2} + 8 t x + 4 t^{2} + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.135 |
$12$ |
$x^{12} + 58 x^{10} + 32 x^{9} + 450 x^{8} - 576 x^{7} + 1888 x^{6} - 1344 x^{5} + 196 x^{4} - 128 x^{3} + 296 x^{2} + 8$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(12 t + 14\right) x^{2} + 8 t x + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.139 |
$12$ |
$x^{12} + 58 x^{10} + 56 x^{9} + 458 x^{8} + 320 x^{7} + 3488 x^{6} + 7552 x^{5} + 12484 x^{4} + 11264 x^{3} + 5800 x^{2} + 1760 x + 552$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(12 t + 14\right) x^{2} + \left(8 t + 8\right) x + 8 t^{2} + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.149 |
$12$ |
$x^{12} + 12 x^{11} + 46 x^{10} + 136 x^{9} + 834 x^{8} + 1936 x^{7} + 3936 x^{6} + 7872 x^{5} + 13876 x^{4} + 15248 x^{3} + 14488 x^{2} + 8160 x + 3624$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t^{2} + 8 t + 2\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 12 t^{2} + 8 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.150 |
$12$ |
$x^{12} + 12 x^{11} + 82 x^{10} + 336 x^{9} + 986 x^{8} + 1760 x^{7} + 2352 x^{6} + 608 x^{5} + 2388 x^{4} + 624 x^{3} + 1736 x^{2} - 248$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 4 t + 14\right) x^{2} + 4 t^{2} + 8 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.16 |
$12$ |
$x^{12} + 18 x^{10} + 152 x^{9} + 10 x^{8} - 576 x^{7} + 928 x^{6} + 3776 x^{5} + 8772 x^{4} + 7296 x^{3} + 6664 x^{2} + 1760 x + 552$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(8 t^{2} + 12 t + 6\right) x^{2} + \left(8 t + 8\right) x + 8 t^{2} + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.192 |
$12$ |
$x^{12} - 6 x^{10} + 8 x^{9} + 558 x^{8} + 672 x^{7} + 3184 x^{6} + 6848 x^{5} + 16164 x^{4} + 19008 x^{3} + 21512 x^{2} + 11936 x + 6392$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(12 t^{2} + 12 t + 6\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 12 t^{2} + 12 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.195 |
$12$ |
$x^{12} - 2 x^{10} + 8 x^{9} + 190 x^{8} + 160 x^{7} - 96 x^{6} + 1824 x^{5} + 3972 x^{4} + 4736 x^{3} + 3512 x^{2} + 2784 x + 2232$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 8 t + 2\right) x^{2} + \left(8 t^{2} + 8\right) x + 4 t^{2} + 4 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.209 |
$12$ |
$x^{12} + 12 x^{11} + 82 x^{10} + 368 x^{9} + 1298 x^{8} + 3056 x^{7} + 6384 x^{6} + 12096 x^{5} + 12372 x^{4} + 7888 x^{3} + 7368 x^{2} + 1408 x + 1384$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(12 t^{2} + 4 t + 14\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 4 t^{2} + 8 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.21 |
$12$ |
$x^{12} + 14 x^{10} - 16 x^{9} + 62 x^{8} + 176 x^{7} - 192 x^{6} + 832 x^{5} + 932 x^{4} + 224 x^{3} + 2040 x^{2} + 3576$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t^{2} + 2\right) x^{2} + 4 t^{2} + 12 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.222 |
$12$ |
$x^{12} + 12 x^{11} + 62 x^{10} + 184 x^{9} + 806 x^{8} + 2688 x^{7} + 5296 x^{6} + 10752 x^{5} + 12324 x^{4} + 13872 x^{3} + 8600 x^{2} + 6752 x + 3032$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(8 t^{2} + 12 t + 10\right) x^{2} + \left(8 t^{2} + 8\right) x + 12 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.23 |
$12$ |
$x^{12} - 8 x^{11} + 78 x^{10} - 16 x^{9} + 250 x^{8} + 176 x^{7} + 624 x^{6} + 512 x^{5} + 308 x^{4} - 192 x^{3} + 312 x^{2} + 1096$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 2\right) x^{2} + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.234 |
$12$ |
$x^{12} + 6 x^{10} + 8 x^{9} + 350 x^{8} + 576 x^{7} + 4704 x^{6} + 8896 x^{5} + 15524 x^{4} + 15360 x^{3} + 14616 x^{2} + 7200 x + 3576$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(12 t^{2} + 8 t + 10\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 4 t^{2} + 12 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.252 |
$12$ |
$x^{12} - 8 x^{11} + 102 x^{10} + 16 x^{9} + 698 x^{8} + 624 x^{7} + 2480 x^{6} + 704 x^{5} + 3764 x^{4} - 192 x^{3} + 3096 x^{2} + 1096$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 8 t + 10\right) x^{2} + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.268 |
$12$ |
$x^{12} + 38 x^{10} - 16 x^{9} + 414 x^{8} + 208 x^{7} + 1696 x^{6} + 1568 x^{5} + 3524 x^{4} + 3040 x^{3} + 4184 x^{2} + 1728 x + 2232$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2\wr C_6$ (as 12T134) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 3, 3, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t^{2} + 10\right) x^{2} + 8 t x + 4 t^{2} + 4 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
