| Label |
$n$ |
Polynomial |
$p$ |
$f$ |
$e$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible Artin slopes |
Visible Swan slopes |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
$\#\Aut(K/\Q_p)$ |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 2.1.16.54o1.2 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 2$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 15, 31, 47]$ |
| 2.1.16.54o1.3 |
$16$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 2$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 15, 31, 47]$ |
| 2.1.16.54o1.4 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 2$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 15, 31, 47]$ |
| 2.1.16.54o1.5 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 18$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{11} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 18$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 15, 31, 47]$ |
| 2.1.16.54o1.16 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 2$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 15, 31, 47]$ |
| 2.1.16.54o1.17 |
$16$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 2$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 15, 31, 47]$ |
| 2.1.16.54o1.18 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 2$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 15, 31, 47]$ |
| 2.1.16.54o1.19 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 18$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{11} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 18$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 15, 31, 47]$ |
| 2.1.16.54o1.386 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.54o1.387 |
$16$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.54o1.389 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.54o1.390 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 22$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 22$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.54o1.400 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.54o1.401 |
$16$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.54o1.403 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 6$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.54o1.404 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 22$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:D_4$ (as 16T410) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3]^{2}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 8 x^{2} + 22$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
