| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.24.117 |
$12$ |
$x^{12} + 12 x^{10} + 8 x^{9} - 198 x^{8} - 328 x^{7} - 872 x^{6} - 2176 x^{5} - 2076 x^{4} - 3664 x^{3} - 2768 x^{2} - 1824 x - 376$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(2 t^{2} + 6 t\right) x^{2} + 4 t x + 12 t^{2} + 12 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.139 |
$12$ |
$x^{12} + 6 x^{10} + 12 x^{9} + 82 x^{8} + 48 x^{7} + 216 x^{6} + 464 x^{5} + 748 x^{4} + 1280 x^{3} + 2728 x^{2} + 2160 x + 3064$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t + 2\right) x^{2} + 4 x + 4 t^{2} + 8 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.149 |
$12$ |
$x^{12} + 4 x^{11} + 18 x^{10} + 136 x^{9} + 206 x^{8} + 368 x^{7} + 1032 x^{6} - 80 x^{5} + 140 x^{4} + 2960 x^{3} + 248 x^{2} - 288 x + 1928$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4\right) x^{3} + \left(2 t + 6\right) x^{2} + 4 t x + 12 t^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.151 |
$12$ |
$x^{12} + 24 x^{10} - 16 x^{9} + 6 x^{8} + 88 x^{7} - 24 x^{6} + 384 x^{5} + 468 x^{4} + 880 x^{3} + 2240 x^{2} + 1728 x + 2392$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(2 t^{2} + 4 t + 4\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.152 |
$12$ |
$x^{12} + 12 x^{11} + 74 x^{10} + 252 x^{9} + 566 x^{8} + 960 x^{7} + 1560 x^{6} + 1520 x^{5} + 1500 x^{4} + 272 x^{3} + 1528 x^{2} + 240 x + 1928$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t^{2} + 6 t + 6\right) x^{2} + 4 x + 12 t^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.156 |
$12$ |
$x^{12} + 12 x^{11} + 66 x^{10} + 208 x^{9} + 454 x^{8} + 800 x^{7} + 1208 x^{6} + 1760 x^{5} + 1868 x^{4} + 1200 x^{3} + 2104 x^{2} + 288 x + 1384$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t + 6\right) x^{2} + 4 t x + 4 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.162 |
$12$ |
$x^{12} + 6 x^{10} + 12 x^{9} + 138 x^{8} + 48 x^{7} + 840 x^{6} + 528 x^{5} + 2652 x^{4} + 640 x^{3} + 3144 x^{2} - 144 x + 1944$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t^{2} + 6 t + 6\right) x^{2} + 4 x + 12 t^{2} + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.168 |
$12$ |
$x^{12} + 24 x^{10} - 20 x^{9} + 66 x^{8} + 328 x^{7} + 480 x^{6} + 976 x^{5} + 1604 x^{4} + 1904 x^{3} + 1968 x^{2} + 1456 x + 1352$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(2 t^{2} + 2 t + 4\right) x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.171 |
$12$ |
$x^{12} + 12 x^{11} + 66 x^{10} + 96 x^{9} + 174 x^{8} + 352 x^{7} + 632 x^{6} + 496 x^{5} + 508 x^{4} + 1328 x^{3} + 568 x^{2} - 320 x + 1096$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(2 t^{2} + 2\right) x^{2} + 4 t^{2} x + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.184 |
$12$ |
$x^{12} + 12 x^{11} + 68 x^{10} + 196 x^{9} + 486 x^{8} + 1144 x^{7} + 1992 x^{6} + 2864 x^{5} + 4244 x^{4} + 5280 x^{3} + 3600 x^{2} + 2512 x + 3128$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t^{2} + 6 t + 4\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.212 |
$12$ |
$x^{12} + 4 x^{10} + 24 x^{9} + 2 x^{8} - 104 x^{7} - 224 x^{6} - 976 x^{5} - 492 x^{4} - 2448 x^{3} - 768 x^{2} - 1600 x - 1048$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(6 t^{2} + 2 t\right) x^{2} + 4 t x + 8 t^{2} + 12 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.23 |
$12$ |
$x^{12} + 12 x^{11} + 56 x^{10} + 68 x^{9} + 182 x^{8} + 568 x^{7} + 896 x^{6} + 1328 x^{5} + 2388 x^{4} + 2880 x^{3} + 2640 x^{2} + 3024 x + 1944$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t^{2} + 2 t\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 12 t^{2} + 12 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.246 |
$12$ |
$x^{12} + 12 x^{10} + 4 x^{9} + 54 x^{8} + 72 x^{7} + 232 x^{6} + 432 x^{5} + 804 x^{4} + 1200 x^{3} + 1936 x^{2} + 1808 x + 1048$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t + 4\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.268 |
$12$ |
$x^{12} + 12 x^{11} + 76 x^{10} + 180 x^{9} + 378 x^{8} + 632 x^{7} + 744 x^{6} + 1008 x^{5} + 1236 x^{4} + 1280 x^{3} + 1488 x^{2} + 912 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(2 t + 4\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.269 |
$12$ |
$x^{12} + 12 x^{11} + 66 x^{10} + 208 x^{9} + 434 x^{8} + 736 x^{7} + 1304 x^{6} + 1984 x^{5} + 2236 x^{4} + 2224 x^{3} + 3128 x^{2} + 864 x + 2232$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t + 6\right) x^{2} + 4 t x + 4 t^{2} + 4 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.275 |
$12$ |
$x^{12} + 4 x^{11} + 78 x^{10} + 260 x^{9} + 610 x^{8} + 768 x^{7} + 1368 x^{6} + 1760 x^{5} + 1180 x^{4} + 1776 x^{3} + 1032 x^{2} + 368 x + 888$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(2 t^{2} + 6\right) x^{2} + 4 x + 8 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.278 |
$12$ |
$x^{12} + 22 x^{10} - 36 x^{9} - 30 x^{8} + 240 x^{7} + 488 x^{6} + 720 x^{5} + 1004 x^{4} + 2080 x^{3} + 1128 x^{2} + 240 x + 1784$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(2 t + 2\right) x^{2} + 4 x + 12 t^{2} + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.281 |
$12$ |
$x^{12} + 4 x^{10} - 8 x^{9} + 150 x^{8} + 40 x^{7} + 408 x^{6} + 112 x^{5} + 2164 x^{4} + 688 x^{3} + 2064 x^{2} - 896 x + 2904$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 6 t + 4\right) x^{2} + 4 t^{2} x + 4 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.294 |
$12$ |
$x^{12} + 26 x^{10} + 110 x^{8} + 256 x^{7} + 296 x^{6} + 992 x^{5} + 1148 x^{4} + 1024 x^{3} + 2232 x^{2} + 288 x + 1384$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t^{2} + 2 t + 6\right) x^{2} + 4 t x + 4 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.30 |
$12$ |
$x^{12} - 8 x^{11} + 4 x^{10} + 184 x^{9} + 426 x^{8} + 264 x^{7} - 296 x^{6} - 656 x^{5} - 908 x^{4} - 816 x^{3} - 1072 x^{2} - 640 x - 376$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + 4 t x + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.35 |
$12$ |
$x^{12} + 2 x^{10} + 12 x^{9} + 78 x^{8} + 16 x^{7} + 312 x^{6} + 336 x^{5} + 748 x^{4} + 1472 x^{3} + 2872 x^{2} + 1264 x + 3624$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 6 t + 2\right) x^{2} + 4 x + 12 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.44 |
$12$ |
$x^{12} + 12 x^{11} + 40 x^{10} - 8 x^{9} - 58 x^{8} + 552 x^{7} + 640 x^{6} + 1328 x^{5} - 12 x^{4} + 1760 x^{3} - 720 x^{2} + 576 x - 104$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 6 t\right) x^{2} + 4 t^{2} x + 4 t^{2} + 12 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.5 |
$12$ |
$x^{12} + 12 x^{9} + 90 x^{8} + 104 x^{7} + 816 x^{6} + 688 x^{5} + 2756 x^{4} + 1840 x^{3} + 4336 x^{2} + 1840 x + 2376$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t^{2} + 4 t + 4\right) x^{2} + \left(4 t + 4\right) x + 8 t^{2} + 12 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.59 |
$12$ |
$x^{12} + 16 x^{10} - 24 x^{9} - 182 x^{8} - 280 x^{7} - 112 x^{6} - 240 x^{5} + 404 x^{4} + 1136 x^{3} + 1104 x^{2} + 64 x + 936$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + 6 t x^{2} + 4 t^{2} x + 4 t^{2} + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.71 |
$12$ |
$x^{12} + 12 x^{11} + 82 x^{10} + 224 x^{9} + 506 x^{8} + 640 x^{7} + 808 x^{6} + 1120 x^{5} + 684 x^{4} + 912 x^{3} + 760 x^{2} - 160 x + 408$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(2 t + 6\right) x^{2} + 4 t x + 4 t^{2} + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.72 |
$12$ |
$x^{12} - 8 x^{9} + 30 x^{8} + 56 x^{7} + 312 x^{6} + 416 x^{5} + 836 x^{4} + 720 x^{3} + 1120 x^{2} - 1568 x + 2744$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t^{2} + 4\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.73 |
$12$ |
$x^{12} + 12 x^{11} + 42 x^{10} + 8 x^{9} - 6 x^{8} + 736 x^{7} + 1192 x^{6} + 384 x^{5} + 1052 x^{4} + 1648 x^{3} + 1080 x^{2} + 320 x + 88$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t^{2} + 6 t + 2\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 4 t^{2} + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.74 |
$12$ |
$x^{12} + 6 x^{10} + 12 x^{9} + 134 x^{8} + 48 x^{7} + 888 x^{6} + 496 x^{5} + 1804 x^{4} + 832 x^{3} + 1352 x^{2} + 496 x + 488$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t^{2} + 6 t + 6\right) x^{2} + 4 x + 8 t^{2} + 4 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.75 |
$12$ |
$x^{12} + 12 x^{11} + 62 x^{10} + 168 x^{9} + 314 x^{8} + 624 x^{7} + 1432 x^{6} + 2720 x^{5} + 3692 x^{4} + 3408 x^{3} + 6664 x^{2} + 3648 x + 5048$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 6 t + 6\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 8 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.77 |
$12$ |
$x^{12} - 8 x^{11} + 30 x^{10} - 4 x^{9} + 186 x^{8} + 80 x^{7} + 392 x^{6} + 976 x^{5} + 620 x^{4} + 1792 x^{3} + 1608 x^{2} + 496 x + 2264$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(2 t^{2} + 6\right) x^{2} + 4 x + 12 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.88 |
$12$ |
$x^{12} + 24 x^{10} + 4 x^{9} - 42 x^{8} + 248 x^{7} - 80 x^{6} + 336 x^{5} + 1508 x^{4} + 208 x^{3} + 2544 x^{2} + 1296 x + 1944$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(2 t^{2} + 4 t + 4\right) x^{2} + \left(4 t + 4\right) x + 12 t^{2} + 12 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.9 |
$12$ |
$x^{12} + 12 x^{11} + 56 x^{10} + 100 x^{9} + 230 x^{8} + 792 x^{7} + 1144 x^{6} + 1152 x^{5} + 3252 x^{4} + 5344 x^{3} + 4000 x^{2} + 4592 x + 4568$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^3:C_6$ (as 12T141) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t^{2} + 6 t\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.115 |
$12$ |
$x^{12} + 12 x^{11} + 44 x^{10} + 56 x^{9} + 210 x^{8} + 816 x^{7} + 424 x^{6} + 768 x^{5} + 292 x^{4} + 720 x^{3} + 496 x^{2} + 96 x + 8$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 6 t\right) x^{2} + \left(8 t + 8\right) x + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.133 |
$12$ |
$x^{12} + 12 x^{11} + 52 x^{10} + 80 x^{9} + 538 x^{8} + 2912 x^{7} + 5960 x^{6} + 6048 x^{5} + 8388 x^{4} + 6960 x^{3} + 8720 x^{2} + 3264 x + 2088$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(10 t^{2} + 14 t + 8\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 8 t^{2} + 8 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.160 |
$12$ |
$x^{12} + 12 x^{11} + 44 x^{10} + 16 x^{9} - 22 x^{8} + 928 x^{7} + 1496 x^{6} - 352 x^{5} - 3436 x^{4} - 3344 x^{3} - 2928 x^{2} - 960 x - 376$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 10 t\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 8 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.186 |
$12$ |
$x^{12} + 12 x^{11} + 28 x^{10} - 96 x^{9} - 2 x^{8} + 1616 x^{7} + 2024 x^{6} + 512 x^{5} + 2036 x^{4} - 1136 x^{3} + 1072 x^{2} - 128 x + 1048$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(10 t^{2} + 6 t\right) x^{2} + 8 t x + 8 t^{2} + 8 t + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.188 |
$12$ |
$x^{12} + 12 x^{11} + 68 x^{10} + 232 x^{9} + 786 x^{8} + 2400 x^{7} + 3112 x^{6} + 5600 x^{5} + 5220 x^{4} + 5296 x^{3} + 3024 x^{2} + 1824 x + 72$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 14 t + 8\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{2} + 8 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.19 |
$12$ |
$x^{12} + 12 x^{11} + 52 x^{10} + 120 x^{9} + 642 x^{8} + 2448 x^{7} + 4792 x^{6} + 5312 x^{5} + 10452 x^{4} + 6736 x^{3} + 6704 x^{2} + 1760 x + 552$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(10 t^{2} + 10 t + 8\right) x^{2} + \left(8 t + 8\right) x + 8 t^{2} + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.199 |
$12$ |
$x^{12} + 12 x^{11} + 68 x^{10} + 224 x^{9} + 746 x^{8} + 1760 x^{7} + 472 x^{6} + 2048 x^{5} + 5732 x^{4} + 176 x^{3} + 3120 x^{2} + 552$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 14 t + 8\right) x^{2} + 8 t^{2} + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.200 |
$12$ |
$x^{12} + 12 x^{11} + 28 x^{10} - 112 x^{9} + 286 x^{8} + 3712 x^{7} + 1064 x^{6} - 5216 x^{5} + 692 x^{4} + 5680 x^{3} + 1200 x^{2} - 576 x + 216$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(10 t^{2} + 14 t\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.201 |
$12$ |
$x^{12} + 12 x^{11} + 68 x^{10} + 232 x^{9} + 694 x^{8} + 1776 x^{7} + 2408 x^{6} + 4320 x^{5} + 3908 x^{4} + 2960 x^{3} + 720 x^{2} + 288 x + 216$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 10 t + 8\right) x^{2} + \left(8 t^{2} + 8\right) x + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.220 |
$12$ |
$x^{12} + 4 x^{11} + 80 x^{10} + 368 x^{9} + 1562 x^{8} + 2992 x^{7} + 3272 x^{6} + 6304 x^{5} + 5876 x^{4} + 3472 x^{3} + 6944 x^{2} + 2728$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(10 t^{2} + 2 t + 12\right) x^{2} + 12 t^{2} + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.241 |
$12$ |
$x^{12} + 4 x^{11} + 56 x^{10} + 544 x^{9} + 1746 x^{8} + 1712 x^{7} + 680 x^{6} + 4352 x^{5} + 5380 x^{4} + 1488 x^{3} + 2944 x^{2} + 936$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(10 t^{2} + 14 t + 4\right) x^{2} + 4 t^{2} + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.246 |
$12$ |
$x^{12} + 4 x^{11} + 96 x^{10} + 576 x^{9} + 1774 x^{8} + 2832 x^{7} + 4008 x^{6} + 6080 x^{5} + 9268 x^{4} + 2256 x^{3} + 8160 x^{2} + 2232$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(2 t^{2} + 14 t + 12\right) x^{2} + 4 t^{2} + 4 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.262 |
$12$ |
$x^{12} + 12 x^{11} + 28 x^{10} - 72 x^{9} + 630 x^{8} + 3264 x^{7} - 3656 x^{6} + 6784 x^{5} + 6580 x^{4} + 2352 x^{3} + 2576 x^{2} + 5216 x + 3128$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(10 t^{2} + 14 t\right) x^{2} + 8 x + 8 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.276 |
$12$ |
$x^{12} + 12 x^{11} + 44 x^{10} + 40 x^{9} + 326 x^{8} + 2176 x^{7} + 328 x^{6} - 2016 x^{5} + 6868 x^{4} + 11952 x^{3} + 2800 x^{2} + 1568 x + 2744$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 14 t\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.281 |
$12$ |
$x^{12} + 12 x^{11} + 68 x^{10} + 224 x^{9} + 510 x^{8} + 1008 x^{7} + 2104 x^{6} + 3456 x^{5} + 3876 x^{4} + 3472 x^{3} + 4528 x^{2} + 256 x + 3128$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 2 t + 8\right) x^{2} + 8 t x + 8 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.29 |
$12$ |
$x^{12} + 12 x^{11} + 52 x^{10} + 96 x^{9} + 462 x^{8} + 1696 x^{7} + 3304 x^{6} + 2624 x^{5} + 8644 x^{4} + 1840 x^{3} + 9040 x^{2} + 3576$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(10 t^{2} + 10 t + 8\right) x^{2} + 8 t^{2} + 8 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.295 |
$12$ |
$x^{12} + 12 x^{11} + 44 x^{10} + 32 x^{9} - 2 x^{8} + 496 x^{7} + 1016 x^{6} + 128 x^{5} + 932 x^{4} + 2448 x^{3} - 688 x^{2} + 256 x + 3128$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 2 t\right) x^{2} + 8 t x + 8 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.30 |
$12$ |
$x^{12} + 12 x^{11} + 28 x^{10} - 72 x^{9} + 386 x^{8} + 2576 x^{7} - 200 x^{6} + 2240 x^{5} + 7508 x^{4} + 3408 x^{3} + 6352 x^{2} + 1760 x + 552$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^3:C_6$ (as 12T141) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(10 t^{2} + 10 t\right) x^{2} + \left(8 t + 8\right) x + 8 t^{2} + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
