| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.24.103 |
$12$ |
$x^{12} + 12 x^{11} + 62 x^{10} + 180 x^{9} + 338 x^{8} + 496 x^{7} + 720 x^{6} + 1024 x^{5} + 1260 x^{4} + 1328 x^{3} + 1368 x^{2} + 1104 x + 536$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 2 t + 6\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{2} + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.109 |
$12$ |
$x^{12} + 12 x^{11} + 62 x^{10} + 188 x^{9} + 418 x^{8} + 768 x^{7} + 1312 x^{6} + 2032 x^{5} + 2988 x^{4} + 3984 x^{3} + 5816 x^{2} + 2544 x + 6392$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 2 t + 6\right) x^{2} + 4 x + 12 t^{2} + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.11 |
$12$ |
$x^{12} - 8 x^{11} + 90 x^{10} - 28 x^{9} + 450 x^{8} + 624 x^{7} + 1760 x^{6} + 768 x^{5} + 636 x^{4} - 384 x^{3} + 2632 x^{2} + 2352 x + 2744$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 2 t + 6\right) x^{2} + 4 x + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.120 |
$12$ |
$x^{12} + 18 x^{10} + 20 x^{9} - 130 x^{8} - 200 x^{7} - 352 x^{6} - 544 x^{5} + 156 x^{4} + 176 x^{3} + 1256 x^{2} + 1424 x + 1384$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(2 t^{2} + 6 t + 2\right) x^{2} + \left(4 t + 4\right) x + 4 t^{2} + 12 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.14 |
$12$ |
$x^{12} + 18 x^{10} - 16 x^{9} - 58 x^{8} + 96 x^{7} + 48 x^{6} + 956 x^{4} + 1280 x^{3} + 2120 x^{2} + 1056 x + 2088$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(2 t^{2} + 4 t + 2\right) x^{2} + 4 t^{2} x + 8 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.147 |
$12$ |
$x^{12} + 26 x^{10} + 32 x^{9} - 34 x^{8} + 80 x^{7} + 144 x^{6} + 496 x^{5} + 828 x^{4} + 384 x^{3} + 872 x^{2} - 64 x + 584$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t^{2} + 6 t + 6\right) x^{2} + 4 t x + 8 t^{2} + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.15 |
$12$ |
$x^{12} + 10 x^{10} + 12 x^{9} + 154 x^{8} + 80 x^{7} + 592 x^{6} + 688 x^{5} + 1084 x^{4} + 544 x^{3} + 648 x^{2} + 432 x + 216$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 6 t + 6\right) x^{2} + 4 x + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.161 |
$12$ |
$x^{12} + 6 x^{10} + 4 x^{9} + 74 x^{8} + 112 x^{7} + 672 x^{6} + 1184 x^{5} + 2620 x^{4} + 2912 x^{3} + 3736 x^{2} + 2256 x + 2232$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t^{2} + 2 t + 6\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 4 t^{2} + 4 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.180 |
$12$ |
$x^{12} + 12 x^{11} + 54 x^{10} + 124 x^{9} + 274 x^{8} + 544 x^{7} + 752 x^{6} + 784 x^{5} + 1980 x^{4} + 208 x^{3} + 3000 x^{2} - 144 x + 1944$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t^{2} + 4 t + 6\right) x^{2} + 4 x + 12 t^{2} + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.199 |
$12$ |
$x^{12} + 12 x^{11} + 82 x^{10} + 268 x^{9} + 518 x^{8} + 912 x^{7} + 1280 x^{6} + 1072 x^{5} + 1164 x^{4} + 912 x^{3} + 392 x^{2} + 1072 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(6 t + 6\right) x^{2} + 4 x + 8 t^{2} + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.250 |
$12$ |
$x^{12} + 12 x^{11} + 58 x^{10} + 116 x^{9} + 374 x^{8} + 648 x^{7} + 1472 x^{6} + 1584 x^{5} + 3036 x^{4} + 2816 x^{3} + 3112 x^{2} + 1776 x + 2088$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(6 t^{2} + 2 t + 2\right) x^{2} + \left(4 t + 4\right) x + 8 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.271 |
$12$ |
$x^{12} + 18 x^{10} - 12 x^{9} + 10 x^{8} + 40 x^{7} + 416 x^{6} + 944 x^{5} + 1516 x^{4} + 2064 x^{3} + 2024 x^{2} + 1904 x + 1016$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(2 t^{2} + 2 t + 2\right) x^{2} + \left(4 t + 4\right) x + 8 t^{2} + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.284 |
$12$ |
$x^{12} + 6 x^{10} - 8 x^{9} + 138 x^{8} + 144 x^{7} + 992 x^{6} + 944 x^{5} + 3052 x^{4} + 2528 x^{3} + 4472 x^{2} + 2208 x + 2264$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t^{2} + 6 t + 6\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 12 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.286 |
$12$ |
$x^{12} - 2 x^{10} + 94 x^{8} + 96 x^{7} + 320 x^{6} - 144 x^{5} - 36 x^{4} - 960 x^{3} - 328 x^{2} - 704 x + 72$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 6 t + 2\right) x^{2} + 4 t x + 8 t^{2} + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.292 |
$12$ |
$x^{12} + 12 x^{11} + 82 x^{10} + 228 x^{9} + 574 x^{8} + 1192 x^{7} + 1776 x^{6} + 2336 x^{5} + 3084 x^{4} + 2816 x^{3} + 2376 x^{2} + 1616 x + 1128$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(2 t + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.37 |
$12$ |
$x^{12} + 6 x^{10} + 12 x^{9} + 114 x^{8} + 48 x^{7} + 960 x^{6} + 560 x^{5} + 3420 x^{4} + 1568 x^{3} + 5784 x^{2} + 1840 x + 3576$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t^{2} + 4 t + 6\right) x^{2} + 4 x + 8 t^{2} + 8 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.65 |
$12$ |
$x^{12} + 12 x^{11} + 54 x^{10} + 124 x^{9} + 238 x^{8} + 448 x^{7} + 912 x^{6} + 1200 x^{5} + 1116 x^{4} + 1168 x^{3} + 472 x^{2} + 304 x - 376$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(6 t^{2} + 2 t + 6\right) x^{2} + 4 x + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.95 |
$12$ |
$x^{12} + 6 x^{10} + 12 x^{9} + 38 x^{8} + 48 x^{7} + 160 x^{6} + 112 x^{5} - 148 x^{4} + 1056 x^{3} - 1672 x^{2} + 1776 x - 1048$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t + 2\right) x^{2} + 4 x + 8 t^{2} + 12 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.108 |
$12$ |
$x^{12} + 4 x^{11} + 66 x^{10} + 472 x^{9} + 1394 x^{8} + 1872 x^{7} + 1344 x^{6} + 1680 x^{5} + 2028 x^{4} + 144 x^{3} + 72 x^{2} + 216$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(8 t^{2} + 10 t + 6\right) x^{2} + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.116 |
$12$ |
$x^{12} + 42 x^{10} + 144 x^{9} + 278 x^{8} + 432 x^{7} + 4992 x^{6} + 352 x^{5} + 5004 x^{4} - 192 x^{3} + 2472 x^{2} + 488$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(8 t^{2} + 14 t + 14\right) x^{2} + 8 t^{2} + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.140 |
$12$ |
$x^{12} + 58 x^{10} - 32 x^{9} + 734 x^{8} - 224 x^{7} + 4992 x^{6} + 192 x^{5} + 8780 x^{4} + 3040 x^{3} + 6120 x^{2} + 3328 x + 1352$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(6 t + 14\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 8 t^{2} + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.141 |
$12$ |
$x^{12} + 12 x^{11} + 90 x^{10} + 440 x^{9} + 1570 x^{8} + 4064 x^{7} + 7552 x^{6} + 8960 x^{5} + 9484 x^{4} + 5232 x^{3} + 3976 x^{2} + 480 x + 536$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(8 t^{2} + 6 t + 14\right) x^{2} + \left(8 t + 8\right) x + 8 t^{2} + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.15 |
$12$ |
$x^{12} + 12 x^{11} + 66 x^{10} + 272 x^{9} + 786 x^{8} + 1232 x^{7} + 1712 x^{6} + 3104 x^{5} + 4012 x^{4} + 2576 x^{3} + 456 x^{2} - 576 x + 216$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(8 t^{2} + 14 t + 6\right) x^{2} + 8 t^{2} x + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.152 |
$12$ |
$x^{12} - 8 x^{11} + 82 x^{10} + 200 x^{9} + 318 x^{8} + 464 x^{7} + 1696 x^{6} + 1904 x^{5} + 3116 x^{4} - 192 x^{3} + 1576 x^{2} + 1096$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(8 t^{2} + 10 t + 6\right) x^{2} + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.154 |
$12$ |
$x^{12} + 12 x^{11} + 94 x^{10} + 440 x^{9} + 1186 x^{8} + 2048 x^{7} + 2976 x^{6} + 3648 x^{5} + 3372 x^{4} + 2736 x^{3} + 1400 x^{2} + 608 x + 88$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(14 t + 10\right) x^{2} + \left(8 t + 8\right) x + 8 t + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.156 |
$12$ |
$x^{12} + 12 x^{11} + 82 x^{10} + 328 x^{9} + 650 x^{8} + 912 x^{7} + 3520 x^{6} + 9216 x^{5} + 9676 x^{4} + 8592 x^{3} + 6568 x^{2} + 1824 x + 1016$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(14 t + 6\right) x^{2} + \left(8 t^{2} + 8\right) x + 8 t^{2} + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.169 |
$12$ |
$x^{12} + 12 x^{11} + 94 x^{10} + 352 x^{9} + 906 x^{8} + 1696 x^{7} + 2832 x^{6} + 4288 x^{5} + 4748 x^{4} + 1904 x^{3} + 3672 x^{2} + 1016$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(6 t + 10\right) x^{2} + 8 t^{2} + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.178 |
$12$ |
$x^{12} + 18 x^{10} + 104 x^{9} + 62 x^{8} + 336 x^{7} + 1712 x^{6} + 2336 x^{5} + 3340 x^{4} + 4096 x^{3} + 4584 x^{2} + 2016 x + 712$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(8 t^{2} + 6 t + 6\right) x^{2} + \left(8 t + 8\right) x + 12 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.191 |
$12$ |
$x^{12} + 12 x^{11} + 82 x^{10} + 280 x^{9} + 626 x^{8} + 1408 x^{7} + 2592 x^{6} + 3104 x^{5} + 3660 x^{4} + 3504 x^{3} + 1448 x^{2} + 1888 x + 1048$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(6 t + 6\right) x^{2} + 8 x + 8 t^{2} + 8 t + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.207 |
$12$ |
$x^{12} + 18 x^{10} + 64 x^{9} + 142 x^{8} + 288 x^{7} + 864 x^{6} + 2432 x^{5} + 4972 x^{4} + 6496 x^{3} + 6536 x^{2} + 3328 x + 1352$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(8 t^{2} + 6 t + 6\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 8 t^{2} + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.211 |
$12$ |
$x^{12} - 8 x^{11} + 98 x^{10} + 40 x^{9} + 78 x^{8} - 368 x^{7} + 800 x^{6} + 560 x^{5} + 1676 x^{4} - 192 x^{3} + 2216 x^{2} + 1096$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(10 t + 6\right) x^{2} + 4 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.235 |
$12$ |
$x^{12} + 12 x^{11} + 82 x^{10} + 256 x^{9} + 474 x^{8} + 832 x^{7} + 1584 x^{6} + 2304 x^{5} + 2380 x^{4} + 2736 x^{3} + 4104 x^{2} + 3128$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(6 t + 6\right) x^{2} + 8 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.250 |
$12$ |
$x^{12} + 42 x^{10} + 88 x^{9} + 422 x^{8} + 1792 x^{7} + 4912 x^{6} + 5248 x^{5} + 8172 x^{4} + 5408 x^{3} + 1928 x^{2} + 1760 x - 1432$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(8 t^{2} + 6 t + 14\right) x^{2} + \left(8 t^{2} + 8\right) x + 12 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.256 |
$12$ |
$x^{12} + 12 x^{11} + 66 x^{10} + 296 x^{9} + 986 x^{8} + 1936 x^{7} + 4384 x^{6} + 10944 x^{5} + 14636 x^{4} + 10896 x^{3} + 6760 x^{2} + 1824 x + 1016$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(8 t^{2} + 14 t + 6\right) x^{2} + \left(8 t^{2} + 8\right) x + 8 t^{2} + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.26 |
$12$ |
$x^{12} + 34 x^{10} - 8 x^{9} + 118 x^{8} - 32 x^{7} + 624 x^{6} + 1312 x^{5} + 1900 x^{4} + 2272 x^{3} + 744 x^{2} + 96 x - 24$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(6 t + 6\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.277 |
$12$ |
$x^{12} + 42 x^{10} + 152 x^{9} + 390 x^{8} + 960 x^{7} + 7504 x^{6} + 7552 x^{5} + 6828 x^{4} + 7328 x^{3} - 1144 x^{2} + 1760 x - 1432$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(8 t^{2} + 14 t + 14\right) x^{2} + \left(8 t^{2} + 8\right) x + 12 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.31 |
$12$ |
$x^{12} + 58 x^{10} + 32 x^{9} + 446 x^{8} - 704 x^{7} + 4800 x^{6} + 1184 x^{5} + 7980 x^{4} + 3360 x^{3} + 7848 x^{2} + 2560 x + 2376$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(14 t + 14\right) x^{2} + 8 t^{2} x + 8 t^{2} + 12 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.32 |
$12$ |
$x^{12} + 12 x^{11} + 90 x^{10} + 416 x^{9} + 1418 x^{8} + 3360 x^{7} + 5520 x^{6} + 7072 x^{5} + 6604 x^{4} + 5872 x^{3} + 5992 x^{2} + 2744$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(8 t^{2} + 6 t + 14\right) x^{2} + 8 t x + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.34 |
$12$ |
$x^{12} + 4 x^{11} + 82 x^{10} + 440 x^{9} + 770 x^{8} + 592 x^{7} + 416 x^{6} + 1488 x^{5} + 1356 x^{4} + 144 x^{3} + 648 x^{2} + 216$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(10 t + 6\right) x^{2} + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.42 |
$12$ |
$x^{12} + 18 x^{10} + 144 x^{9} - 10 x^{8} - 1136 x^{7} - 1792 x^{6} - 6080 x^{5} - 5140 x^{4} - 8064 x^{3} - 4344 x^{2} - 3200 x - 1048$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(8 t^{2} + 14 t + 6\right) x^{2} + 8 t x + 8 t^{2} + 12 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.66 |
$12$ |
$x^{12} + 34 x^{10} + 48 x^{9} - 218 x^{8} - 1648 x^{7} - 3584 x^{6} - 6400 x^{5} - 7028 x^{4} - 7424 x^{3} - 5112 x^{2} - 3200 x - 1048$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(14 t + 6\right) x^{2} + 8 t x + 8 t^{2} + 12 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.94 |
$12$ |
$x^{12} + 12 x^{11} + 106 x^{10} + 520 x^{9} + 1706 x^{8} + 4016 x^{7} + 8768 x^{6} + 14432 x^{5} + 19820 x^{4} + 18256 x^{3} + 16840 x^{2} + 7968 x + 3576$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_2^4.A_4$ (as 12T92) |
$6$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(14 t + 14\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{2} + 8 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
