| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.12.20 |
$12$ |
$x^{12} - 2 x^{11} - 172 x^{9} - 172 x^{8} + 2112 x^{7} + 7968 x^{6} + 13568 x^{5} + 22320 x^{4} + 29216 x^{3} + 22912 x^{2} + 18624 x + 11200$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3}\right) x + 4 t^{4} + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.12.4 |
$12$ |
$x^{12} + 6 x^{11} + 24 x^{10} + 84 x^{9} + 196 x^{8} + 336 x^{7} + 768 x^{6} + 2144 x^{5} + 4784 x^{4} + 8032 x^{3} + 9600 x^{2} + 6976 x + 2240$ |
$2$ |
$2$ |
$6$ |
$12$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[2]$ |
$[2, 2, 2, 2, 2]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t + 2\right) x + 4 t^{3} + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
| 2.12.18.11 |
$12$ |
$x^{12} + 8 x^{11} + 20 x^{10} - 144 x^{9} + 8668 x^{8} - 36032 x^{7} + 196448 x^{6} - 771200 x^{5} + 1475568 x^{4} - 3364224 x^{3} + 5649728 x^{2} + 12790528 x + 10676800$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4}\right) x + 8 t^{2} + 8 t + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.13 |
$12$ |
$x^{12} + 32 x^{11} + 532 x^{10} + 2944 x^{9} + 24252 x^{8} + 59520 x^{7} + 363872 x^{6} + 263936 x^{5} + 2174704 x^{4} - 449536 x^{3} + 8127808 x^{2} + 9509888 x + 9117760$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t + 4\right) x + 8 t^{4} + 8 t^{2} + 14$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.18 |
$12$ |
$x^{12} + 32 x^{11} + 356 x^{10} + 1376 x^{9} + 940 x^{8} + 18208 x^{6} + 37120 x^{5} + 219376 x^{4} + 87552 x^{3} + 2043200 x^{2} - 2284032 x + 610624$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{4} + 4\right) x + 8 t^{5} + 4 t^{4} + 8 t^{2} + 12 t + 2$ |
$[2, 0]$ |
$[1]$ |
| 2.12.18.7 |
$12$ |
$x^{12} + 20 x^{11} - 32 x^{10} - 1752 x^{9} - 1228 x^{8} + 14560 x^{7} + 191168 x^{6} + 549056 x^{5} + 1551280 x^{4} + 2624320 x^{3} + 4892416 x^{2} + 3340928 x + 2780608$ |
$2$ |
$2$ |
$6$ |
$18$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4\right) x + 12 t^{5} + 4 t^{3} + 12 t^{2} + 4 t + 6$ |
$[2, 0]$ |
$[1]$ |
| 2.12.24.111 |
$12$ |
$x^{12} + 12 x^{11} + 46 x^{10} + 52 x^{9} + 86 x^{8} + 544 x^{7} + 896 x^{6} + 1744 x^{5} + 2660 x^{4} + 4944 x^{3} + 4088 x^{2} + 3888 x + 4568$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 4 t + 2\right) x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.153 |
$12$ |
$x^{12} + 6 x^{10} + 12 x^{9} + 30 x^{8} + 48 x^{7} + 144 x^{6} + 256 x^{5} + 372 x^{4} + 480 x^{3} + 600 x^{2} + 304 x + 88$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{2} + \left(4 t + 4\right) x + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.203 |
$12$ |
$x^{12} + 10 x^{10} - 8 x^{9} + 118 x^{8} + 64 x^{7} + 672 x^{6} + 416 x^{5} + 2292 x^{4} + 2048 x^{3} + 3656 x^{2} + 1184 x + 1016$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 6\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 8 t^{2} + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.261 |
$12$ |
$x^{12} - 8 x^{11} + 78 x^{10} + 56 x^{9} + 90 x^{8} + 496 x^{7} + 688 x^{6} + 1200 x^{5} + 1780 x^{4} + 2272 x^{3} + 2168 x^{2} + 1600 x + 1608$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 4 t + 2\right) x^{2} + 4 t^{2} x + 12 t^{2} + 4 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.266 |
$12$ |
$x^{12} + 14 x^{10} + 8 x^{9} - 2 x^{8} + 80 x^{7} - 224 x^{6} + 160 x^{5} + 1316 x^{4} + 2592 x^{3} + 5240 x^{2} + 3424 x + 6392$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t^{2} + 4 t + 2\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.274 |
$12$ |
$x^{12} + 12 x^{11} + 62 x^{10} + 96 x^{9} + 254 x^{8} + 416 x^{7} + 1200 x^{6} + 1232 x^{5} + 836 x^{4} + 3664 x^{3} + 1688 x^{2} + 224 x + 3576$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t^{2} + 2\right) x^{2} + 4 t x + 4 t^{2} + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.299 |
$12$ |
$x^{12} - 8 x^{11} + 26 x^{10} + 394 x^{8} + 64 x^{7} + 576 x^{6} + 160 x^{5} + 1972 x^{4} + 1632 x^{3} + 2888 x^{2} - 768 x + 712$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(4 t^{2} + 6\right) x^{2} + 4 t x + 12 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.319 |
$12$ |
$x^{12} + 26 x^{10} - 12 x^{9} + 194 x^{8} + 352 x^{7} + 208 x^{6} + 1776 x^{5} + 1524 x^{4} + 1312 x^{3} + 3880 x^{2} + 560 x - 1048$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t^{2} + 6\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 12 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.61 |
$12$ |
$x^{12} + 4 x^{11} - 2 x^{10} + 96 x^{9} + 450 x^{8} + 784 x^{7} + 992 x^{6} + 1488 x^{5} + 1556 x^{4} + 1744 x^{3} + 1112 x^{2} + 288 x + 1384$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4\right) x^{3} + \left(4 t^{2} + 4 t + 2\right) x^{2} + 4 t x + 4 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.80 |
$12$ |
$x^{12} + 34 x^{10} - 28 x^{9} + 74 x^{8} + 304 x^{7} + 240 x^{6} + 528 x^{5} + 1204 x^{4} - 128 x^{3} + 776 x^{2} + 1264 x - 1272$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 4 t^{2} + 12 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.92 |
$12$ |
$x^{12} + 6 x^{10} + 54 x^{8} + 192 x^{6} + 64 x^{5} + 852 x^{4} + 64 x^{3} + 1144 x^{2} + 128 x + 3128$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 2 x^{2} + 4 t x + 8 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.96 |
$12$ |
$x^{12} + 18 x^{10} + 122 x^{8} + 32 x^{7} + 352 x^{6} + 112 x^{5} + 308 x^{4} - 96 x^{3} - 24 x^{2} - 608 x - 248$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 6\right) x^{2} + 4 t x + 4 t^{2} + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.30.1 |
$12$ |
$x^{12} + 4 x^{11} + 64 x^{10} + 352 x^{9} + 198 x^{8} - 384 x^{7} + 1184 x^{6} + 1984 x^{5} + 604 x^{4} + 2608 x^{3} + 1728 x^{2} + 1768$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + 8 t x^{2} + 12 t^{2} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.10 |
$12$ |
$x^{12} + 4 x^{11} + 28 x^{10} + 112 x^{9} + 498 x^{8} + 880 x^{7} + 3568 x^{6} + 2720 x^{5} + 9916 x^{4} + 5392 x^{3} + 7472 x^{2} + 5888 x + 1784$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4\right) x^{3} + \left(4 t^{2} + 12\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 12 t^{2} + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.102 |
$12$ |
$x^{12} + 4 x^{11} + 76 x^{10} + 448 x^{9} + 838 x^{8} + 880 x^{7} - 976 x^{6} - 800 x^{5} - 1012 x^{4} + 208 x^{3} + 688 x^{2} - 64 x + 8$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(12 t + 4\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.111 |
$12$ |
$x^{12} + 4 x^{11} + 76 x^{10} + 488 x^{9} + 694 x^{8} + 784 x^{7} + 2448 x^{6} + 1792 x^{5} + 1292 x^{4} + 4624 x^{3} - 1680 x^{2} + 2144 x + 72$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(12 t + 4\right) x^{2} + 8 x + 8 t^{2} + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.119 |
$12$ |
$x^{12} + 4 x^{11} + 40 x^{10} + 320 x^{9} + 1154 x^{8} + 2032 x^{7} + 2752 x^{6} + 5376 x^{5} + 7740 x^{4} + 4368 x^{3} + 7072 x^{2} + 3384$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(12 t^{2} + 4 t\right) x^{2} + 12 t^{2} + 4 t + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.138 |
$12$ |
$x^{12} + 4 x^{11} + 76 x^{10} + 472 x^{9} + 742 x^{8} + 1424 x^{7} + 2096 x^{6} + 3584 x^{5} + 1036 x^{4} + 3344 x^{3} - 592 x^{2} + 928 x - 376$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(12 t + 4\right) x^{2} + \left(8 t^{2} + 8\right) x + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.15 |
$12$ |
$x^{12} + 4 x^{11} + 80 x^{10} + 280 x^{9} + 1118 x^{8} + 2240 x^{7} + 5136 x^{6} + 8096 x^{5} + 10556 x^{4} + 12528 x^{3} + 10464 x^{2} + 6240 x + 2376$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t^{2} + 8\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{2} + 12 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.159 |
$12$ |
$x^{12} + 4 x^{11} + 100 x^{10} + 296 x^{9} + 1306 x^{8} + 1856 x^{7} + 3760 x^{6} + 3232 x^{5} + 2940 x^{4} + 1328 x^{3} + 1104 x^{2} + 416 x + 88$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + 12 x^{2} + \left(8 t^{2} + 8\right) x + 4 t^{2} + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.161 |
$12$ |
$x^{12} + 4 x^{11} + 88 x^{10} + 264 x^{9} + 982 x^{8} + 1792 x^{7} + 4192 x^{6} + 5376 x^{5} + 7868 x^{4} + 7600 x^{3} + 6624 x^{2} + 3936 x + 1384$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + 8 x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 4 t^{2} + 8 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.167 |
$12$ |
$x^{12} + 4 x^{11} + 52 x^{10} + 352 x^{9} + 1254 x^{8} + 2736 x^{7} + 4112 x^{6} + 6208 x^{5} + 7324 x^{4} + 4432 x^{3} + 8784 x^{2} + 4072$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(12 t^{2} + 4 t + 4\right) x^{2} + 12 t^{2} + 12 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.174 |
$12$ |
$x^{12} + 4 x^{11} + 56 x^{10} + 192 x^{9} + 478 x^{8} + 1344 x^{7} + 2672 x^{6} + 2368 x^{5} + 3644 x^{4} + 4464 x^{3} + 1920 x^{2} + 2432 x + 2376$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + 4 t^{2} x^{2} + \left(8 t^{2} + 8 t\right) x + 8 t^{2} + 12 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.198 |
$12$ |
$x^{12} + 4 x^{11} + 100 x^{10} + 376 x^{9} + 1382 x^{8} + 2896 x^{7} + 4240 x^{6} + 5696 x^{5} + 3596 x^{4} + 3728 x^{3} + 1296 x^{2} + 928 x - 376$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t + 12\right) x^{2} + \left(8 t^{2} + 8\right) x + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.200 |
$12$ |
$x^{12} + 4 x^{11} + 92 x^{10} + 448 x^{9} + 1602 x^{8} + 3040 x^{7} + 4864 x^{6} + 4992 x^{5} + 6620 x^{4} + 4272 x^{3} + 4304 x^{2} + 1792 x + 888$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t^{2} + 8 t + 12\right) x^{2} + 8 t^{2} x + 8 t^{2} + 4 t + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.209 |
$12$ |
$x^{12} + 4 x^{11} + 48 x^{10} + 208 x^{9} + 630 x^{8} + 1504 x^{7} + 2752 x^{6} + 3136 x^{5} + 4188 x^{4} + 4080 x^{3} + 832 x^{2} - 576 x + 424$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + 8 t^{2} x^{2} + 8 t^{2} x + 4 t^{2} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.220 |
$12$ |
$x^{12} + 4 x^{11} + 92 x^{10} + 408 x^{9} + 1638 x^{8} + 3312 x^{7} + 6576 x^{6} + 10048 x^{5} + 9852 x^{4} + 10704 x^{3} + 7536 x^{2} + 2976 x + 2728$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t^{2} + 4 t + 12\right) x^{2} + \left(8 t + 8\right) x + 12 t^{2} + 4 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.23 |
$12$ |
$x^{12} + 4 x^{11} + 52 x^{10} + 440 x^{9} + 1602 x^{8} + 3744 x^{7} + 7616 x^{6} + 11488 x^{5} + 11356 x^{4} + 9904 x^{3} + 5744 x^{2} + 2528 x + 888$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(12 t^{2} + 8 t + 4\right) x^{2} + \left(8 t^{2} + 8\right) x + 8 t^{2} + 4 t + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.244 |
$12$ |
$x^{12} + 4 x^{11} + 64 x^{10} + 176 x^{9} + 226 x^{8} + 928 x^{7} + 1600 x^{6} + 544 x^{5} + 3356 x^{4} + 2544 x^{3} + 2688 x^{2} + 1792 x + 3064$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(8 t^{2} + 8 t\right) x + 4 t^{2} + 8 t + 14$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.268 |
$12$ |
$x^{12} + 4 x^{11} + 56 x^{10} + 352 x^{9} + 766 x^{8} + 1280 x^{7} + 1648 x^{6} + 640 x^{5} + 380 x^{4} + 2032 x^{3} + 1792 x^{2} + 2432 x + 2376$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t^{2} + 8 t\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 8 t^{2} + 12 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.279 |
$12$ |
$x^{12} + 4 x^{11} + 64 x^{10} + 256 x^{9} + 130 x^{8} + 528 x^{7} + 512 x^{6} + 1056 x^{5} + 140 x^{4} + 1232 x^{3} + 384 x^{2} - 576 x + 216$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + 4 t x^{2} + 8 t^{2} x + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.35 |
$12$ |
$x^{12} + 4 x^{11} + 100 x^{10} + 312 x^{9} + 1430 x^{8} + 1920 x^{7} + 6224 x^{6} + 6400 x^{5} + 6908 x^{4} + 7728 x^{3} + 2896 x^{2} + 1440 x + 1768$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + 12 x^{2} + \left(8 t + 8\right) x + 12 t^{2} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.46 |
$12$ |
$x^{12} + 4 x^{11} + 88 x^{10} + 336 x^{9} + 786 x^{8} + 848 x^{7} + 1600 x^{6} + 1248 x^{5} + 972 x^{4} + 1104 x^{3} + 160 x^{2} + 536$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t + 8\right) x^{2} + 8 t^{2} + 6$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.58 |
$12$ |
$x^{12} + 4 x^{11} + 52 x^{10} + 512 x^{9} + 1798 x^{8} + 2736 x^{7} + 3440 x^{6} + 6656 x^{5} + 6492 x^{4} + 4432 x^{3} + 8976 x^{2} + 4072$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(12 t^{2} + 12 t + 4\right) x^{2} + 12 t^{2} + 12 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.63 |
$12$ |
$x^{12} + 4 x^{11} + 40 x^{10} + 504 x^{9} + 1750 x^{8} + 1648 x^{7} + 3328 x^{6} + 11296 x^{5} + 3964 x^{4} + 12624 x^{3} + 7200 x^{2} + 4320 x + 4072$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(12 t^{2} + 12 t\right) x^{2} + 8 x + 12 t^{2} + 12 t + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
| 2.12.30.87 |
$12$ |
$x^{12} + 4 x^{11} + 72 x^{10} + 432 x^{9} + 1462 x^{8} + 2976 x^{7} + 4736 x^{6} + 6144 x^{5} + 6364 x^{4} + 3440 x^{3} + 2912 x^{2} - 576 x + 424$ |
$2$ |
$4$ |
$3$ |
$30$ |
$C_2^4:A_4$ (as 12T87) |
$3$ |
$1$ |
$[3, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(8 t^{2} + 8 t + 8\right) x^{2} + 8 t^{2} x + 4 t^{2} + 10$ |
$[7, 4, 0]$ |
$[1, 1]$ |
