| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.24.105 |
$12$ |
$x^{12} + 8 x^{10} - 8 x^{9} + 42 x^{8} + 16 x^{7} + 320 x^{6} + 384 x^{5} + 1236 x^{4} + 1376 x^{3} + 3152 x^{2} + 2816 x + 3624$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t + 4\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.122 |
$12$ |
$x^{12} - 8 x^{11} + 16 x^{10} + 100 x^{9} + 314 x^{8} + 848 x^{7} + 1784 x^{6} + 2704 x^{5} + 3588 x^{4} + 4128 x^{3} + 3360 x^{2} + 2128 x + 1928$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(6 t^{2} + 4 t + 4\right) x^{2} + \left(4 t^{2} + 4\right) x + 12 t^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.124 |
$12$ |
$x^{12} + 4 x^{10} + 4 x^{9} + 114 x^{8} + 72 x^{7} + 480 x^{6} + 752 x^{5} + 2340 x^{4} + 2672 x^{3} + 4672 x^{2} + 2480 x + 2728$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 6 t + 4\right) x^{2} + \left(4 t^{2} + 4\right) x + 12 t^{2} + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.134 |
$12$ |
$x^{12} + 12 x^{11} + 48 x^{10} + 56 x^{9} + 10 x^{8} + 192 x^{7} + 520 x^{6} + 688 x^{5} + 932 x^{4} + 688 x^{3} + 576 x^{2} + 224 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t^{2} + 4 t + 4\right) x^{2} + 4 t^{2} x + 4 t^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.159 |
$12$ |
$x^{12} + 16 x^{10} - 36 x^{9} - 74 x^{8} + 112 x^{7} - 328 x^{6} - 320 x^{5} + 516 x^{4} - 896 x^{3} - 288 x^{2} + 1008 x - 648$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + 2 t x^{2} + 4 x + 12 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.17 |
$12$ |
$x^{12} + 12 x^{11} + 72 x^{10} + 156 x^{9} + 406 x^{8} + 848 x^{7} + 1400 x^{6} + 1792 x^{5} + 2468 x^{4} + 4336 x^{3} + 3520 x^{2} + 3728 x + 5048$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(2 t^{2} + 4\right) x^{2} + \left(4 t^{2} + 4\right) x + 12 t^{2} + 8 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.185 |
$12$ |
$x^{12} + 12 x^{11} + 48 x^{10} + 68 x^{9} + 34 x^{8} + 184 x^{7} + 784 x^{6} + 1200 x^{5} + 2580 x^{4} + 3072 x^{3} + 3088 x^{2} + 2288 x + 1352$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t^{2} + 4\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.188 |
$12$ |
$x^{12} + 12 x^{11} + 56 x^{10} + 140 x^{9} + 262 x^{8} + 480 x^{7} + 712 x^{6} + 800 x^{5} + 932 x^{4} + 880 x^{3} + 576 x^{2} + 432 x + 216$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 4\right) x^{2} + 4 x + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.189 |
$12$ |
$x^{12} + 16 x^{10} + 36 x^{9} + 22 x^{8} + 320 x^{7} + 952 x^{6} + 1552 x^{5} + 1972 x^{4} + 1216 x^{3} + 1920 x^{2} + 816 x + 1016$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(6 t^{2} + 2 t + 4\right) x^{2} + 4 x + 8 t^{2} + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.196 |
$12$ |
$x^{12} + 4 x^{11} + 88 x^{9} + 106 x^{8} + 208 x^{7} + 792 x^{6} + 416 x^{5} + 564 x^{4} + 1200 x^{3} - 704 x^{2} - 704 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4\right) x^{3} + 2 t x^{2} + 4 t x + 8 t^{2} + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.198 |
$12$ |
$x^{12} + 8 x^{10} + 6 x^{8} - 80 x^{7} - 296 x^{6} + 112 x^{5} + 692 x^{4} + 1408 x^{3} + 1376 x^{2} + 1216 x + 3576$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t^{2} + 2 t\right) x^{2} + 4 t x + 8 t^{2} + 8 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.210 |
$12$ |
$x^{12} - 8 x^{11} + 24 x^{10} + 68 x^{9} + 178 x^{8} + 456 x^{7} + 1368 x^{6} + 1744 x^{5} + 3172 x^{4} + 4624 x^{3} + 4576 x^{2} + 4080 x + 3624$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(2 t^{2} + 4 t + 4\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 12 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.235 |
$12$ |
$x^{12} + 12 x^{10} - 48 x^{9} + 58 x^{8} + 96 x^{7} - 528 x^{6} + 144 x^{5} + 308 x^{4} - 1632 x^{3} - 32 x^{2} + 256 x - 1432$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + 2 t^{2} x^{2} + 4 t^{2} x + 12 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.236 |
$12$ |
$x^{12} + 12 x^{11} + 64 x^{10} + 124 x^{9} + 78 x^{8} + 336 x^{7} + 904 x^{6} + 960 x^{5} + 2148 x^{4} + 2928 x^{3} + 1056 x^{2} + 2416 x + 2904$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + 6 t x^{2} + 4 x + 4 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.237 |
$12$ |
$x^{12} + 12 x^{11} + 60 x^{10} + 60 x^{9} + 142 x^{8} + 704 x^{7} + 800 x^{6} + 560 x^{5} + 2788 x^{4} + 3696 x^{3} + 1440 x^{2} + 3888 x + 4568$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + 2 t^{2} x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.241 |
$12$ |
$x^{12} + 12 x^{11} + 56 x^{10} + 132 x^{9} + 222 x^{8} + 520 x^{7} + 1216 x^{6} + 1936 x^{5} + 3044 x^{4} + 4736 x^{3} + 4240 x^{2} + 2992 x + 3032$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 4\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.242 |
$12$ |
$x^{12} - 12 x^{10} + 4 x^{9} + 190 x^{8} + 144 x^{7} + 64 x^{6} + 512 x^{5} + 740 x^{4} + 1152 x^{3} + 1152 x^{2} + 1008 x + 408$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t^{2} + 6 t\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 4 t^{2} + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.245 |
$12$ |
$x^{12} + 12 x^{11} + 60 x^{10} + 84 x^{9} + 118 x^{8} + 416 x^{7} + 568 x^{6} + 464 x^{5} + 900 x^{4} + 1392 x^{3} + 464 x^{2} + 944 x + 1048$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(2 t^{2} + 2 t\right) x^{2} + 4 x + 8 t^{2} + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.255 |
$12$ |
$x^{12} + 12 x^{11} + 64 x^{10} + 124 x^{9} + 86 x^{8} + 192 x^{7} - 8 x^{6} - 720 x^{5} - 540 x^{4} - 944 x^{3} - 1536 x^{2} - 144 x - 648$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + 6 t x^{2} + \left(4 t + 4\right) x + 12 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.265 |
$12$ |
$x^{12} - 4 x^{10} + 4 x^{9} + 62 x^{8} + 48 x^{7} - 16 x^{6} + 224 x^{5} + 980 x^{4} + 768 x^{3} + 640 x^{2} + 1776 x + 2904$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 4 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.272 |
$12$ |
$x^{12} + 4 x^{11} + 64 x^{10} + 380 x^{9} + 914 x^{8} + 1376 x^{7} + 2576 x^{6} + 3968 x^{5} + 3140 x^{4} + 3280 x^{3} + 3344 x^{2} + 624 x + 1352$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(6 t^{2} + 6 t + 4\right) x^{2} + 4 x + 8 t^{2} + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.285 |
$12$ |
$x^{12} + 4 x^{11} + 64 x^{10} + 300 x^{9} + 838 x^{8} + 1400 x^{7} + 2624 x^{6} + 3840 x^{5} + 4068 x^{4} + 4768 x^{3} + 3664 x^{2} + 2608 x + 2264$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(6 t^{2} + 2 t + 4\right) x^{2} + \left(4 t + 4\right) x + 8 t^{2} + 4 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.29 |
$12$ |
$x^{12} - 12 x^{10} - 8 x^{9} + 46 x^{8} + 48 x^{7} + 208 x^{6} + 416 x^{5} + 884 x^{4} + 736 x^{3} + 608 x^{2} + 256 x + 344$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 6 t^{2} x^{2} + 4 t^{2} x + 4 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.297 |
$12$ |
$x^{12} + 12 x^{11} + 40 x^{10} + 4 x^{9} - 50 x^{8} + 248 x^{7} + 168 x^{6} + 960 x^{5} + 1108 x^{4} + 2304 x^{3} + 1536 x^{2} + 1872 x + 1048$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 2 t\right) x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.3 |
$12$ |
$x^{12} - 8 x^{9} + 6 x^{8} - 16 x^{7} + 320 x^{6} + 448 x^{5} + 548 x^{4} - 32 x^{3} + 528 x^{2} + 248$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t^{2} + 4\right) x^{2} + 4 t^{2} x + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.42 |
$12$ |
$x^{12} - 8 x^{10} + 12 x^{9} + 142 x^{8} - 64 x^{7} - 112 x^{6} + 640 x^{5} + 1668 x^{4} + 416 x^{3} + 3952 x^{2} + 240 x + 1784$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 6 t\right) x^{2} + 4 x + 12 t^{2} + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.6 |
$12$ |
$x^{12} + 12 x^{11} + 52 x^{10} + 108 x^{9} + 206 x^{8} + 480 x^{7} + 712 x^{6} + 896 x^{5} + 1076 x^{4} + 1008 x^{3} + 784 x^{2} + 496 x + 248$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 2 t + 4\right) x^{2} + 4 x + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.70 |
$12$ |
$x^{12} - 8 x^{11} + 4 x^{10} + 164 x^{9} + 358 x^{8} + 320 x^{7} + 768 x^{6} + 2240 x^{5} + 2036 x^{4} - 608 x^{3} - 960 x^{2} + 1520 x + 2904$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(6 t^{2} + 4 t\right) x^{2} + \left(4 t^{2} + 4\right) x + 4 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.76 |
$12$ |
$x^{12} - 8 x^{11} + 68 x^{10} + 48 x^{9} + 214 x^{8} + 544 x^{7} + 992 x^{6} + 1872 x^{5} + 2180 x^{4} + 2528 x^{3} + 1760 x^{2} + 896 x + 888$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + 6 t^{2} x^{2} + 4 t^{2} x + 8 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.93 |
$12$ |
$x^{12} + 4 x^{10} + 68 x^{9} - 54 x^{8} - 600 x^{7} - 280 x^{6} + 768 x^{5} + 1844 x^{4} + 1040 x^{3} + 1552 x^{2} + 1424 x + 936$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + \left(4 t + 4\right) x + 4 t^{2} + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.97 |
$12$ |
$x^{12} - 12 x^{10} + 4 x^{9} + 70 x^{8} - 48 x^{7} + 144 x^{6} + 800 x^{5} + 1460 x^{4} + 448 x^{3} + 1632 x^{2} + 3376 x + 3576$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 5/2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 6 t^{2} x^{2} + \left(4 t^{2} + 4\right) x + 4 t^{2} + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.98 |
$12$ |
$x^{12} + 4 x^{11} + 60 x^{10} + 204 x^{9} + 250 x^{8} + 840 x^{7} + 1160 x^{6} + 1296 x^{5} + 2004 x^{4} + 1568 x^{3} + 1040 x^{2} + 912 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + 2 t^{2} x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.33.111 |
$12$ |
$x^{12} + 24 x^{11} + 264 x^{10} + 1048 x^{9} + 2694 x^{8} + 4576 x^{7} + 7808 x^{6} + 10208 x^{5} + 13404 x^{4} + 8544 x^{3} + 15008 x^{2} + 1888 x + 13032$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(8 t^{2} + 12 t + 8\right) x^{2} + \left(8 t + 8\right) x + 24 t^{2} + 4 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.126 |
$12$ |
$x^{12} + 24 x^{11} + 216 x^{10} + 920 x^{9} + 2318 x^{8} + 5792 x^{7} + 10720 x^{6} + 20064 x^{5} + 20348 x^{4} + 31840 x^{3} + 23072 x^{2} + 19040 x + 23048$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 x^{3} + \left(12 t + 8\right) x^{2} + \left(8 t + 8\right) x + 8 t^{2} + 28 t + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.129 |
$12$ |
$x^{12} + 24 x^{11} + 192 x^{10} + 536 x^{9} + 382 x^{8} + 1440 x^{7} - 128 x^{6} + 4704 x^{5} + 2748 x^{4} + 4704 x^{3} + 4544 x^{2} + 3168 x + 16456$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t x^{2} + \left(8 t + 8\right) x + 24 t^{2} + 4 t + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.132 |
$12$ |
$x^{12} + 8 x^{11} + 268 x^{10} + 1904 x^{9} + 2042 x^{8} + 4512 x^{7} + 15280 x^{6} + 10944 x^{5} + 19932 x^{4} + 43424 x^{3} + 17072 x^{2} + 28480 x + 44824$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t + 8\right) x^{3} + \left(8 t + 4\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 28 t^{2} + 20 t + 22$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.135 |
$12$ |
$x^{12} + 24 x^{11} + 252 x^{10} + 624 x^{9} + 1602 x^{8} + 960 x^{7} + 6768 x^{6} + 5184 x^{5} + 7548 x^{4} + 12448 x^{3} + 8688 x^{2} + 6976 x + 3384$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(8 t^{2} + 4\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 12 t^{2} + 4 t + 14$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.136 |
$12$ |
$x^{12} + 20 x^{10} - 16 x^{9} + 378 x^{8} + 256 x^{7} + 4848 x^{6} + 5376 x^{5} + 26748 x^{4} + 21248 x^{3} + 59280 x^{2} + 22720 x + 47832$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t + 12\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 28 t^{2} + 28 t + 22$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.155 |
$12$ |
$x^{12} + 24 x^{11} + 216 x^{10} + 920 x^{9} + 2118 x^{8} + 3488 x^{7} + 3872 x^{6} + 4960 x^{5} + 5980 x^{4} + 8800 x^{3} + 2336 x^{2} - 1952 x - 6936$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 x^{3} + \left(4 t + 8\right) x^{2} + \left(8 t + 8\right) x + 8 t^{2} + 20 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.159 |
$12$ |
$x^{12} - 16 x^{11} + 76 x^{10} + 368 x^{9} + 618 x^{8} + 736 x^{7} + 4048 x^{6} + 1088 x^{5} + 5788 x^{4} + 5120 x^{3} + 2160 x^{2} + 4416 x + 2264$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 4 x^{2} + \left(8 t^{2} + 8 t\right) x + 12 t^{2} + 4 t + 6$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.16 |
$12$ |
$x^{12} + 88 x^{10} - 424 x^{9} + 110 x^{8} + 320 x^{7} + 1056 x^{6} + 8032 x^{5} + 12604 x^{4} + 24832 x^{3} + 22304 x^{2} + 20832 x + 31496$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(4 t + 8\right) x^{2} + \left(8 t + 8\right) x + 24 t^{2} + 12 t + 26$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.2 |
$12$ |
$x^{12} + 64 x^{10} - 296 x^{9} - 2018 x^{8} - 3776 x^{7} - 6976 x^{6} - 11680 x^{5} - 9348 x^{4} - 7936 x^{3} - 5696 x^{2} + 2400 x + 72$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 t x^{3} + 12 t x^{2} + \left(8 t + 8\right) x + 8 t^{2} + 20 t + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.214 |
$12$ |
$x^{12} + 8 x^{11} + 20 x^{10} + 752 x^{9} + 3026 x^{8} + 8320 x^{7} + 19696 x^{6} + 35904 x^{5} + 49084 x^{4} + 64480 x^{3} + 69904 x^{2} + 37184 x + 60792$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + \left(8 t^{2} + 8 t + 12\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 28 t^{2} + 20 t + 30$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.217 |
$12$ |
$x^{12} - 4 x^{10} - 16 x^{9} - 30 x^{8} + 192 x^{7} + 1456 x^{6} + 3840 x^{5} + 11676 x^{4} + 14720 x^{3} + 29680 x^{2} + 9408 x + 24696$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(8 t^{2} + 4\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 28 t^{2} + 28 t + 14$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.225 |
$12$ |
$x^{12} + 8 x^{11} - 4 x^{10} + 432 x^{9} + 1578 x^{8} + 4800 x^{7} + 11056 x^{6} + 14400 x^{5} + 17244 x^{4} + 18016 x^{3} + 4976 x^{2} - 4032 x - 2216$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + \left(8 t^{2} + 4\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 12 t^{2} + 20 t + 6$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.231 |
$12$ |
$x^{12} + 100 x^{10} - 400 x^{9} + 58 x^{8} - 608 x^{7} + 1872 x^{6} + 6208 x^{5} + 10332 x^{4} + 15808 x^{3} + 31888 x^{2} + 28480 x + 44824$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(8 t + 12\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 28 t^{2} + 20 t + 22$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.232 |
$12$ |
$x^{12} + 8 x^{11} + 292 x^{10} + 1712 x^{9} + 3906 x^{8} + 4448 x^{7} + 15024 x^{6} + 12992 x^{5} + 14524 x^{4} + 22560 x^{3} + 14288 x^{2} + 3648 x + 6584$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t + 8\right) x^{3} + 12 x^{2} + \left(8 t^{2} + 8 t\right) x + 12 t^{2} + 20 t + 14$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.242 |
$12$ |
$x^{12} + 24 x^{11} + 240 x^{10} + 664 x^{9} + 766 x^{8} + 2400 x^{7} + 608 x^{6} + 2016 x^{5} - 708 x^{4} + 2656 x^{3} - 2240 x^{2} + 2400 x + 72$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(8 t^{2} + 12 t\right) x^{2} + \left(8 t + 8\right) x + 8 t^{2} + 20 t + 10$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.252 |
$12$ |
$x^{12} + 88 x^{10} - 296 x^{9} - 1370 x^{8} - 1472 x^{7} - 4896 x^{6} - 3488 x^{5} + 2972 x^{4} - 10496 x^{3} + 32 x^{2} + 5472 x - 1048$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(12 t + 8\right) x^{2} + \left(8 t + 8\right) x + 24 t^{2} + 20 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
| 2.12.33.293 |
$12$ |
$x^{12} + 24 x^{11} + 216 x^{10} + 920 x^{9} + 2166 x^{8} + 4256 x^{7} + 7712 x^{6} + 11872 x^{5} + 15900 x^{4} + 19552 x^{3} + 14112 x^{2} + 9824 x + 8872$ |
$2$ |
$4$ |
$3$ |
$33$ |
$C_2^3.(C_2\times A_4)$ (as 12T104) |
$3$ |
$1$ |
$[3, 4]$ |
$[2, 2, 3, 7/2, 7/2, 4]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 8 x^{3} + \left(4 t + 8\right) x^{2} + \left(8 t + 8\right) x + 8 t^{2} + 20 t + 18$ |
$[8, 4, 0]$ |
$[1, 1]$ |
