| Label |
$n$ |
Polynomial |
$p$ |
$e$ |
$f$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible slopes |
Slope content |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
| 2.16.44.5 |
$16$ |
$x^{16} + 4 x^{15} + 16 x^{14} + 28 x^{12} + 64 x^{11} + 76 x^{10} + 48 x^{9} + 224 x^{8} + 168 x^{7} + 232 x^{6} + 96 x^{5} + 440 x^{4} + 112 x^{3} + 168 x^{2} + 196$ |
$2$ |
$8$ |
$2$ |
$44$ |
$C_4^2:C_2$ (as 16T30) |
$2$ |
$1$ |
$[2, 3, 7/2]$ |
$[2, 3, 3, 7/2]^{2}$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 14 x^{4} + \left(8 t + 8\right) x^{3} + \left(4 t + 8\right) x^{2} + 14$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
| 2.16.48.13 |
$16$ |
$x^{16} + 4 x^{12} + 4 x^{10} + 10 x^{8} + 8 x^{6} + 8 x^{2} + 8 x + 14$ |
$2$ |
$16$ |
$1$ |
$48$ |
$C_4^2:C_2$ (as 16T30) |
$2$ |
$1$ |
$[2, 3, 3, 7/2]$ |
$[2, 3, 3, 7/2]^{2}$ |
$t + 1$ |
$x^{16} + 4 x^{12} + 4 x^{10} + 10 x^{8} + 8 x^{6} + 8 x^{2} + 8 x + 14$ |
$[33, 26, 24, 8, 0]$ |
$[1, 2, 1]$ |
| 2.16.52.12 |
$16$ |
$x^{16} + 8 x^{14} + 4 x^{10} + 8 x^{9} + 10 x^{8} + 8 x^{6} + 8 x^{5} + 26$ |
$2$ |
$16$ |
$1$ |
$52$ |
$C_4^2:C_2$ (as 16T30) |
$2$ |
$1$ |
$[2, 3, 3, 4]$ |
$[2, 3, 3, 4]^{2}$ |
$t + 1$ |
$x^{16} + 8 x^{14} + 4 x^{10} + 8 x^{9} + 10 x^{8} + 8 x^{6} + 8 x^{5} + 26$ |
$[37, 26, 24, 8, 0]$ |
$[1, 2, 1]$ |
| 2.16.52.13 |
$16$ |
$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 12 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 30$ |
$2$ |
$16$ |
$1$ |
$52$ |
$C_4^2:C_2$ (as 16T30) |
$2$ |
$1$ |
$[2, 3, 3, 4]$ |
$[2, 3, 3, 4]^{2}$ |
$t + 1$ |
$x^{16} + 8 x^{15} + 8 x^{14} + 8 x^{13} + 4 x^{12} + 12 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{5} + 30$ |
$[37, 26, 24, 8, 0]$ |
$[1, 2, 1]$ |
| 2.16.52.14 |
$16$ |
$x^{16} - 8 x^{15} + 88 x^{14} - 104 x^{13} + 276 x^{12} - 48 x^{11} + 48 x^{10} + 224 x^{9} - 56 x^{8} + 400 x^{7} - 32 x^{6} + 368 x^{5} + 152 x^{4} - 64 x^{3} + 604$ |
$2$ |
$8$ |
$2$ |
$52$ |
$C_4^2:C_2$ (as 16T30) |
$2$ |
$1$ |
$[3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 12 x^{6} + 8 t x^{5} + \left(4 t + 4\right) x^{4} + 8 x^{3} + 28 t + 10$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
| 2.16.54.20 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 14$ |
$2$ |
$16$ |
$1$ |
$54$ |
$C_4^2:C_2$ (as 16T30) |
$2$ |
$1$ |
$[2, 3, 7/2, 4]$ |
$[2, 3, 7/2, 4]^{2}$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 2 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 14$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
