| 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 |
| 2.1.16.40c4.26 |
$16$ |
$x^{16} + 4 x^{15} + 2 x^{14} + 2 x^{12} + 4 x^{11} + 4 x^{9} + 2 x^{8} + 8 x^{4} + 8 x^{3} + 2$ |
$2$ |
$1$ |
$16$ |
$40$ |
$C_2^6.\SD_{16}$ (as 16T1284) |
$4$ |
$1$ |
$[2, 2, 2, \frac{13}{4}]$ |
$[1,1,1,\frac{9}{4}]$ |
$[2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{4}$ |
$[1,1,1,1,2,2,2,\frac{9}{4}]^{4}$ |
$[2,3,3,3]_{4}$ |
$[1,2,2,2]_{4}$ |
$2$ |
$t + 1$ |
$x^{16} + 4 x^{15} + 2 x^{14} + 2 x^{12} + 4 x^{11} + 4 x^{9} + 2 x^{8} + 8 x^{4} + 8 x^{3} + 2$ |
$[25, 14, 12, 8, 0]$ |
$[4, 1]$ |
$z^{14} + z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 23, 39]$ |
| 2.1.16.40c4.45 |
$16$ |
$x^{16} + 2 x^{14} + 4 x^{13} + 2 x^{12} + 4 x^{9} + 2 x^{8} + 8 x^{3} + 6$ |
$2$ |
$1$ |
$16$ |
$40$ |
$(D_4\times C_2^3).Q_{16}$ (as 16T1255) |
$4$ |
$1$ |
$[2, 2, 2, \frac{13}{4}]$ |
$[1,1,1,\frac{9}{4}]$ |
$[2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{4}$ |
$[1,1,1,1,2,2,2,\frac{9}{4}]^{4}$ |
$[2,3,3,3]_{4}$ |
$[1,2,2,2]_{4}$ |
$2$ |
$t + 1$ |
$x^{16} + 2 x^{14} + 4 x^{13} + 2 x^{12} + 4 x^{9} + 2 x^{8} + 8 x^{3} + 6$ |
$[25, 14, 12, 8, 0]$ |
$[4, 1]$ |
$z^{14} + z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 14, 32]$ |
| 2.1.16.40c4.46 |
$16$ |
$x^{16} + 2 x^{14} + 4 x^{13} + 2 x^{12} + 4 x^{9} + 2 x^{8} + 8 x^{4} + 8 x^{3} + 6$ |
$2$ |
$1$ |
$16$ |
$40$ |
$(D_4\times C_2^3).Q_{16}$ (as 16T1255) |
$4$ |
$1$ |
$[2, 2, 2, \frac{13}{4}]$ |
$[1,1,1,\frac{9}{4}]$ |
$[2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{4}$ |
$[1,1,1,1,2,2,2,\frac{9}{4}]^{4}$ |
$[2,3,3,3]_{4}$ |
$[1,2,2,2]_{4}$ |
$2$ |
$t + 1$ |
$x^{16} + 2 x^{14} + 4 x^{13} + 2 x^{12} + 4 x^{9} + 2 x^{8} + 8 x^{4} + 8 x^{3} + 6$ |
$[25, 14, 12, 8, 0]$ |
$[4, 1]$ |
$z^{14} + z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 14, 32]$ |
| 2.1.16.40c4.47 |
$16$ |
$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 2 x^{12} + 4 x^{9} + 2 x^{8} + 6$ |
$2$ |
$1$ |
$16$ |
$40$ |
$(D_4\times C_2^3).Q_{16}$ (as 16T1255) |
$4$ |
$1$ |
$[2, 2, 2, \frac{13}{4}]$ |
$[1,1,1,\frac{9}{4}]$ |
$[2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{4}$ |
$[1,1,1,1,2,2,2,\frac{9}{4}]^{4}$ |
$[2,3,3,3]_{4}$ |
$[1,2,2,2]_{4}$ |
$2$ |
$t + 1$ |
$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 2 x^{12} + 4 x^{9} + 2 x^{8} + 6$ |
$[25, 14, 12, 8, 0]$ |
$[4, 1]$ |
$z^{14} + z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 14, 32]$ |
| 2.1.16.40c4.48 |
$16$ |
$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 2 x^{12} + 4 x^{9} + 2 x^{8} + 8 x^{4} + 6$ |
$2$ |
$1$ |
$16$ |
$40$ |
$(D_4\times C_2^3).Q_{16}$ (as 16T1255) |
$4$ |
$1$ |
$[2, 2, 2, \frac{13}{4}]$ |
$[1,1,1,\frac{9}{4}]$ |
$[2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{4}$ |
$[1,1,1,1,2,2,2,\frac{9}{4}]^{4}$ |
$[2,3,3,3]_{4}$ |
$[1,2,2,2]_{4}$ |
$2$ |
$t + 1$ |
$x^{16} + 4 x^{15} + 2 x^{14} + 4 x^{13} + 2 x^{12} + 4 x^{9} + 2 x^{8} + 8 x^{4} + 6$ |
$[25, 14, 12, 8, 0]$ |
$[4, 1]$ |
$z^{14} + z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 14, 32]$ |
| 2.1.16.40c4.54 |
$16$ |
$x^{16} + 2 x^{14} + 2 x^{12} + 4 x^{11} + 4 x^{9} + 2 x^{8} + 8 x^{4} + 8 x^{3} + 6$ |
$2$ |
$1$ |
$16$ |
$40$ |
$C_2^6.\SD_{16}$ (as 16T1284) |
$4$ |
$1$ |
$[2, 2, 2, \frac{13}{4}]$ |
$[1,1,1,\frac{9}{4}]$ |
$[2, 2, 2, 2, 3, 3, 3, \frac{13}{4}]^{4}$ |
$[1,1,1,1,2,2,2,\frac{9}{4}]^{4}$ |
$[2,3,3,3]_{4}$ |
$[1,2,2,2]_{4}$ |
$2$ |
$t + 1$ |
$x^{16} + 2 x^{14} + 2 x^{12} + 4 x^{11} + 4 x^{9} + 2 x^{8} + 8 x^{4} + 8 x^{3} + 6$ |
$[25, 14, 12, 8, 0]$ |
$[4, 1]$ |
$z^{14} + z^6 + z^2 + 1,z + 1$ |
$[1, 2, 7, 14, 32]$ |
