| 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 |
| 7.10.1.0a1.1 |
$10$ |
$x^{10} + x^{6} + x^{5} + 4 x^{4} + x^{3} + 2 x^{2} + 3 x + 3$ |
$7$ |
$10$ |
$1$ |
$0$ |
$C_{10}$ (as 10T1) |
$10$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{10}$ |
$[\ ]^{10}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{10} + t^{6} + t^{5} + 4 t^{4} + t^{3} + 2 t^{2} + 3 t + 3$ |
$x - 7$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 7.5.2.5a1.1 |
$10$ |
$( x^{5} + x + 4 )^{2} + 7 x$ |
$7$ |
$5$ |
$2$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$[\ ]_{2}^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + t + 4$ |
$x^{2} + 7 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 7.5.2.5a1.2 |
$10$ |
$( x^{5} + x + 4 )^{2} + 7$ |
$7$ |
$5$ |
$2$ |
$5$ |
$C_{10}$ (as 10T1) |
$5$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{5}$ |
$[\ ]_{2}^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + t + 4$ |
$x^{2} + 7$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 7.2.5.8a1.1 |
$10$ |
$( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$5$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$[\ ]_{5}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t^{2} + 6 t + 3$ |
$x^{5} + 7$ |
$[0]$ |
$[2]$ |
$z^4 + 5 z^3 + 3 z^2 + 3 z + 5$ |
undefined |
| 7.1.10.9a1.1 |
$10$ |
$x^{10} + 7$ |
$7$ |
$1$ |
$10$ |
$9$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$2$ |
$t + 4$ |
$x^{10} + 7$ |
$[0]$ |
$[4]$ |
$z^9 + 3 z^8 + 3 z^7 + z^6 + z^2 + 3 z + 3$ |
undefined |
| 7.1.10.9a1.2 |
$10$ |
$x^{10} + 21$ |
$7$ |
$1$ |
$10$ |
$9$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$10$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{10}^{4}$ |
$[\ ]_{10}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$2$ |
$t + 4$ |
$x^{10} + 21$ |
$[0]$ |
$[4]$ |
$z^9 + 3 z^8 + 3 z^7 + z^6 + z^2 + 3 z + 3$ |
undefined |
