| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.24.169 |
$12$ |
$x^{12} - 2 x^{10} + 4 x^{9} + 118 x^{8} + 56 x^{7} + 176 x^{6} + 656 x^{5} + 1628 x^{4} + 2064 x^{3} + 2904 x^{2} + 1456 x + 1352$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T55) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 6 t + 2\right) x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.174 |
$12$ |
$x^{12} + 4 x^{11} + 18 x^{10} + 140 x^{9} + 178 x^{8} + 648 x^{7} + 1104 x^{6} + 1392 x^{5} + 2060 x^{4} + 2752 x^{3} + 2024 x^{2} + 1872 x + 1048$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T55) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4\right) x^{3} + \left(2 t + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.21 |
$12$ |
$x^{12} + 12 x^{11} + 70 x^{10} + 132 x^{9} + 194 x^{8} + 552 x^{7} + 848 x^{6} + 688 x^{5} + 940 x^{4} + 1088 x^{3} + 856 x^{2} + 1264 x + 888$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T55) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(2 t + 2\right) x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.223 |
$12$ |
$x^{12} + 12 x^{11} + 58 x^{10} + 156 x^{9} + 434 x^{8} + 1248 x^{7} + 2240 x^{6} + 2752 x^{5} + 4412 x^{4} + 4944 x^{3} + 3944 x^{2} + 2672 x + 2904$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T55) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 6 t + 6\right) x^{2} + \left(4 t + 4\right) x + 4 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.225 |
$12$ |
$x^{12} - 8 x^{11} + 86 x^{10} - 36 x^{9} + 606 x^{8} + 1264 x^{7} + 1760 x^{6} + 3408 x^{5} + 3724 x^{4} + 3616 x^{3} + 4024 x^{2} + 2256 x + 2088$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T55) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(6 t^{2} + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 8 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.231 |
$12$ |
$x^{12} + 4 x^{11} + 18 x^{10} + 188 x^{9} + 338 x^{8} + 1112 x^{7} + 1504 x^{6} + 2480 x^{5} + 2572 x^{4} + 3424 x^{3} + 1960 x^{2} + 1872 x + 1048$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T55) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4\right) x^{3} + \left(6 t + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.291 |
$12$ |
$x^{12} + 10 x^{10} + 4 x^{9} + 86 x^{8} + 40 x^{7} + 608 x^{6} + 624 x^{5} + 2076 x^{4} + 1712 x^{3} + 3304 x^{2} + 2416 x + 712$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T55) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 2 t + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 12 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.295 |
$12$ |
$x^{12} + 12 x^{11} + 62 x^{10} + 188 x^{9} + 434 x^{8} + 936 x^{7} + 1776 x^{6} + 2608 x^{5} + 3500 x^{4} + 4128 x^{3} + 3800 x^{2} + 2640 x + 2232$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T55) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{2} + 2 t + 6\right) x^{2} + \left(4 t + 4\right) x + 4 t^{2} + 4 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.296 |
$12$ |
$x^{12} + 12 x^{11} + 46 x^{10} + 52 x^{9} + 26 x^{8} + 184 x^{7} + 176 x^{6} + 384 x^{5} + 732 x^{4} + 992 x^{3} + 1368 x^{2} + 784 x + 536$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T55) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 x^{3} + \left(4 t^{2} + 2 t + 2\right) x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{2} + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.303 |
$12$ |
$x^{12} + 12 x^{11} + 82 x^{10} + 268 x^{9} + 574 x^{8} + 1056 x^{7} + 1920 x^{6} + 2976 x^{5} + 3436 x^{4} + 3632 x^{3} + 2888 x^{2} + 1456 x + 1352$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T55) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(6 t + 6\right) x^{2} + \left(4 t + 4\right) x + 8 t^{2} + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.306 |
$12$ |
$x^{12} + 4 x^{11} + 14 x^{10} + 148 x^{9} + 346 x^{8} + 816 x^{7} + 880 x^{6} + 1216 x^{5} + 956 x^{4} + 688 x^{3} + 504 x^{2} + 144 x + 216$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T55) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4\right) x^{3} + \left(2 t^{2} + 4 t + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.311 |
$12$ |
$x^{12} - 8 x^{11} + 78 x^{10} + 116 x^{9} - 14 x^{8} - 48 x^{7} + 1504 x^{6} + 3216 x^{5} + 2716 x^{4} + 2880 x^{3} + 3160 x^{2} + 1904 x + 1016$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T55) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 6 t + 2\right) x^{2} + \left(4 t + 4\right) x + 8 t^{2} + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.43 |
$12$ |
$x^{12} + 14 x^{10} + 4 x^{9} + 86 x^{8} + 96 x^{7} + 480 x^{6} + 832 x^{5} + 2316 x^{4} + 3264 x^{3} + 5976 x^{2} + 4432 x + 4072$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T55) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(2 t^{2} + 2 t + 6\right) x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 12 t^{2} + 12 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.66 |
$12$ |
$x^{12} + 10 x^{10} + 36 x^{9} + 50 x^{8} - 40 x^{7} + 384 x^{6} + 1456 x^{5} + 1308 x^{4} + 1200 x^{3} + 1800 x^{2} + 2736 x + 3128$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T55) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(6 t^{2} + 2 t + 2\right) x^{2} + \left(4 t + 4\right) x + 8 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
