| 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 |
| 7.16.1.0a1.1 |
$16$ |
$x^{16} + 4 x^{8} + 5 x^{7} + 3 x^{6} + 4 x^{5} + x^{4} + 6 x^{3} + 2 x^{2} + 4 x + 3$ |
$7$ |
$16$ |
$1$ |
$0$ |
$C_{16}$ (as 16T1) |
$16$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{16}$ |
$[\ ]^{16}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{16} + 4 t^{8} + 5 t^{7} + 3 t^{6} + 4 t^{5} + t^{4} + 6 t^{3} + 2 t^{2} + 4 t + 3$ |
$x - 7$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 7.8.2.8a1.1 |
$16$ |
$( x^{8} + 4 x^{3} + 6 x^{2} + 2 x + 3 )^{2} + 7 x$ |
$7$ |
$8$ |
$2$ |
$8$ |
$C_{16}$ (as 16T1) |
$8$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{8}$ |
$[\ ]_{2}^{8}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{8} + 4 t^{3} + 6 t^{2} + 2 t + 3$ |
$x^{2} + 7 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 7.8.2.8a1.2 |
$16$ |
$( x^{8} + 4 x^{3} + 6 x^{2} + 2 x + 3 )^{2} + 7$ |
$7$ |
$8$ |
$2$ |
$8$ |
$C_8\times C_2$ (as 16T5) |
$8$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{8}$ |
$[\ ]_{2}^{8}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{8} + 4 t^{3} + 6 t^{2} + 2 t + 3$ |
$x^{2} + 7$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 7.4.4.12a1.1 |
$16$ |
$( x^{4} + 5 x^{2} + 4 x + 3 )^{4} + 7 x^{2}$ |
$7$ |
$4$ |
$4$ |
$12$ |
$C_8: C_2$ (as 16T6) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$[\ ]_{4}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{4} + 5 t^{2} + 4 t + 3$ |
$x^{4} + 7 t^{2}$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 7.4.4.12a1.2 |
$16$ |
$( x^{4} + 5 x^{2} + 4 x + 3 )^{4} + 7 x$ |
$7$ |
$4$ |
$4$ |
$12$ |
$C_{16} : C_2$ (as 16T22) |
$8$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{8}$ |
$[\ ]_{4}^{8}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$8$ |
$t^{4} + 5 t^{2} + 4 t + 3$ |
$x^{4} + 7 t^{3}$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 7.4.4.12a1.3 |
$16$ |
$( x^{4} + 5 x^{2} + 4 x + 3 )^{4} + 7$ |
$7$ |
$4$ |
$4$ |
$12$ |
$C_4:C_4$ (as 16T8) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$[\ ]_{4}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{4} + 5 t^{2} + 4 t + 3$ |
$x^{4} + 7$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 7.2.8.14a1.1 |
$16$ |
$( x^{2} + 6 x + 3 )^{8} + 7 x$ |
$7$ |
$2$ |
$8$ |
$14$ |
$C_8.C_8$ (as 16T124) |
$8$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{8}$ |
$[\ ]_{8}^{8}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$8$ |
$t^{2} + 6 t + 3$ |
$x^{8} + 42 t + 7$ |
$[0]$ |
$[1]$ |
$z^7 + z^6 + 1$ |
undefined |
| 7.2.8.14a1.2 |
$16$ |
$( x^{2} + 6 x + 3 )^{8} + 7$ |
$7$ |
$2$ |
$8$ |
$14$ |
$D_{8}$ (as 16T13) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + 6 t + 3$ |
$x^{8} + 7$ |
$[0]$ |
$[1]$ |
$z^7 + z^6 + 1$ |
undefined |
| 7.2.8.14a1.3 |
$16$ |
$( x^{2} + 6 x + 3 )^{8} + 7 x + 7$ |
$7$ |
$2$ |
$8$ |
$14$ |
$C_8.C_8$ (as 16T124) |
$8$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{8}$ |
$[\ ]_{8}^{8}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$8$ |
$t^{2} + 6 t + 3$ |
$x^{8} + 35 t + 28$ |
$[0]$ |
$[1]$ |
$z^7 + z^6 + 1$ |
undefined |
| 7.2.8.14a1.4 |
$16$ |
$( x^{2} + 6 x + 3 )^{8} + 7 x + 28$ |
$7$ |
$2$ |
$8$ |
$14$ |
$C_8.C_4$ (as 16T49) |
$4$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{4}$ |
$[\ ]_{8}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$8$ |
$t^{2} + 6 t + 3$ |
$x^{8} + 14 t + 28$ |
$[0]$ |
$[1]$ |
$z^7 + z^6 + 1$ |
undefined |
| 7.2.8.14a1.5 |
$16$ |
$( x^{2} + 6 x + 3 )^{8} + 14 x + 42$ |
$7$ |
$2$ |
$8$ |
$14$ |
$Q_{16}$ (as 16T14) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + 6 t + 3$ |
$x^{8} + 14 t + 42$ |
$[0]$ |
$[1]$ |
$z^7 + z^6 + 1$ |
undefined |
| 7.1.16.15a1.1 |
$16$ |
$x^{16} + 7$ |
$7$ |
$1$ |
$16$ |
$15$ |
$\SD_{32}$ (as 16T55) |
$2$ |
$16$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{16}^{2}$ |
$[\ ]_{16}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 4$ |
$x^{16} + 7$ |
$[0]$ |
$[2]$ |
$z^{15} + 2 z^{14} + z^{13} + 2 z^8 + 4 z^7 + 2 z^6 + z + 2$ |
undefined |
| 7.1.16.15a1.2 |
$16$ |
$x^{16} + 21$ |
$7$ |
$1$ |
$16$ |
$15$ |
$\SD_{32}$ (as 16T55) |
$2$ |
$16$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{16}^{2}$ |
$[\ ]_{16}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 4$ |
$x^{16} + 21$ |
$[0]$ |
$[2]$ |
$z^{15} + 2 z^{14} + z^{13} + 2 z^8 + 4 z^7 + 2 z^6 + z + 2$ |
undefined |
