| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.12.24.114 |
$12$ |
$x^{12} + 14 x^{10} + 12 x^{9} + 22 x^{8} - 32 x^{7} + 272 x^{6} + 832 x^{5} + 796 x^{4} + 800 x^{3} + 952 x^{2} + 1392 x + 1096$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T61) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t^{2} + 2 t + 2\right) x^{2} + \left(4 t + 4\right) x + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.165 |
$12$ |
$x^{12} + 6 x^{10} - 8 x^{9} + 154 x^{8} + 144 x^{7} + 944 x^{6} + 784 x^{5} + 1868 x^{4} + 1184 x^{3} + 1560 x^{2} + 480 x + 344$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T61) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(6 t^{2} + 6 t + 6\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 4 t^{2} + 4 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.202 |
$12$ |
$x^{12} - 8 x^{11} + 22 x^{10} + 68 x^{9} + 382 x^{8} + 896 x^{7} + 1312 x^{6} + 1376 x^{5} + 1308 x^{4} + 1344 x^{3} + 312 x^{2} + 464 x - 376$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T61) |
$6$ |
$1$ |
$[2, 3]$ |
$[2, 2, 3, 3]^{6}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(6 t^{2} + 4 t + 6\right) x^{2} + \left(4 t^{2} + 4\right) x + 8 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.208 |
$12$ |
$x^{12} + 22 x^{10} - 48 x^{9} - 2 x^{8} - 96 x^{7} + 160 x^{6} + 240 x^{5} + 492 x^{4} + 992 x^{3} + 600 x^{2} + 704 x + 552$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T61) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(2 t + 2\right) x^{2} + 4 t x + 8 t^{2} + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.213 |
$12$ |
$x^{12} - 8 x^{11} + 30 x^{10} - 24 x^{9} + 306 x^{8} - 32 x^{7} + 688 x^{6} + 16 x^{5} + 940 x^{4} + 320 x^{3} + 1144 x^{2} + 288 x + 88$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T61) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t^{2} x^{3} + \left(2 t^{2} + 6\right) x^{2} + 4 t^{2} x + 8 t + 6$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.24.27 |
$12$ |
$x^{12} + 22 x^{10} + 48 x^{9} + 66 x^{8} + 240 x^{7} + 640 x^{6} + 1184 x^{5} + 3724 x^{4} + 1984 x^{3} + 5816 x^{2} + 928 x + 3576$ |
$2$ |
$4$ |
$3$ |
$24$ |
$C_4^2:C_6$ (as 12T61) |
$3$ |
$1$ |
$[2, 3]$ |
$[2, 2, 2, 3, 3]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + \left(4 t^{2} + 4 t\right) x + 4 t^{2} + 12 t + 14$ |
$[5, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.123 |
$12$ |
$x^{12} + 12 x^{11} + 66 x^{10} + 224 x^{9} + 618 x^{8} + 1216 x^{7} + 2128 x^{6} + 2624 x^{5} + 3244 x^{4} + 2736 x^{3} + 3656 x^{2} + 3128$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^2:C_6$ (as 12T61) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(8 t^{2} + 6 t + 6\right) x^{2} + 8 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.155 |
$12$ |
$x^{12} + 58 x^{10} + 8 x^{9} + 654 x^{8} + 848 x^{7} + 3984 x^{6} + 5984 x^{5} + 9708 x^{4} + 7808 x^{3} + 6856 x^{2} + 2016 x + 712$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^2:C_6$ (as 12T61) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(6 t + 14\right) x^{2} + \left(8 t + 8\right) x + 12 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.20 |
$12$ |
$x^{12} + 12 x^{11} + 106 x^{10} + 472 x^{9} + 1682 x^{8} + 4000 x^{7} + 7200 x^{6} + 8896 x^{5} + 7852 x^{4} + 5616 x^{3} + 2248 x^{2} + 480 x + 536$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^2:C_6$ (as 12T61) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(6 t + 14\right) x^{2} + \left(8 t + 8\right) x + 8 t^{2} + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.229 |
$12$ |
$x^{12} + 12 x^{11} + 78 x^{10} + 304 x^{9} + 930 x^{8} + 2000 x^{7} + 3600 x^{6} + 5568 x^{5} + 6348 x^{4} + 5648 x^{3} + 4440 x^{2} + 2368 x + 536$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^2:C_6$ (as 12T61) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(8 t^{2} + 6 t + 10\right) x^{2} + \left(8 t^{2} + 8 t\right) x + 8 t^{2} + 6$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.249 |
$12$ |
$x^{12} + 18 x^{10} + 88 x^{9} + 134 x^{8} + 352 x^{7} + 1712 x^{6} + 3808 x^{5} + 4300 x^{4} + 2656 x^{3} + 872 x^{2} + 96 x - 24$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^2:C_6$ (as 12T61) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(8 t^{2} + 6 t + 6\right) x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.263 |
$12$ |
$x^{12} + 42 x^{10} + 128 x^{9} + 398 x^{8} + 512 x^{7} + 6464 x^{6} + 3168 x^{5} + 13836 x^{4} + 6176 x^{3} + 10408 x^{2} + 2560 x + 2376$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^2:C_6$ (as 12T61) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(8 t^{2} + 14 t + 14\right) x^{2} + 8 t^{2} x + 8 t^{2} + 12 t + 10$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.275 |
$12$ |
$x^{12} + 34 x^{10} + 48 x^{9} - 282 x^{8} - 1552 x^{7} - 1184 x^{6} - 352 x^{5} + 492 x^{4} - 192 x^{3} + 72 x^{2} + 488$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^2:C_6$ (as 12T61) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(14 t + 6\right) x^{2} + 8 t^{2} + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
| 2.12.27.49 |
$12$ |
$x^{12} + 12 x^{11} + 78 x^{10} + 392 x^{9} + 1322 x^{8} + 3184 x^{7} + 7392 x^{6} + 12416 x^{5} + 14508 x^{4} + 12624 x^{3} + 7544 x^{2} + 4768 x + 3128$ |
$2$ |
$4$ |
$3$ |
$27$ |
$C_4^2:C_6$ (as 12T61) |
$3$ |
$1$ |
$[2, 7/2]$ |
$[2, 2, 3, 7/2, 7/2]^{3}$ |
$t^{3} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(8 t^{2} + 14 t + 10\right) x^{2} + \left(8 t^{2} + 8\right) x + 8 t + 14$ |
$[6, 2, 0]$ |
$[1, 1]$ |
