| 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 |
| 7.22.1.0a1.1 |
$22$ |
$x^{22} + x^{12} + 6 x^{11} + 5 x^{10} + 3 x^{9} + 5 x^{8} + 2 x^{7} + 3 x^{6} + 4 x^{5} + 6 x^{4} + 5 x^{3} + 5 x^{2} + 4 x + 3$ |
$7$ |
$22$ |
$1$ |
$0$ |
$C_{22}$ (as 22T1) |
$22$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{22}$ |
$[\ ]^{22}$ |
$[\ ]$ |
$[\ ]$ |
$22$ |
$t^{22} + t^{12} + 6 t^{11} + 5 t^{10} + 3 t^{9} + 5 t^{8} + 2 t^{7} + 3 t^{6} + 4 t^{5} + 6 t^{4} + 5 t^{3} + 5 t^{2} + 4 t + 3$ |
$x - 7$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 7.11.2.11a1.1 |
$22$ |
$( x^{11} + x + 4 )^{2} + 7 x$ |
$7$ |
$11$ |
$2$ |
$11$ |
$C_{22}$ (as 22T1) |
$11$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{11}$ |
$[\ ]_{2}^{11}$ |
$[\ ]$ |
$[\ ]$ |
$22$ |
$t^{11} + t + 4$ |
$x^{2} + 7 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 7.11.2.11a1.2 |
$22$ |
$( x^{11} + x + 4 )^{2} + 7$ |
$7$ |
$11$ |
$2$ |
$11$ |
$C_{22}$ (as 22T1) |
$11$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{11}$ |
$[\ ]_{2}^{11}$ |
$[\ ]$ |
$[\ ]$ |
$22$ |
$t^{11} + t + 4$ |
$x^{2} + 7$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 7.2.11.20a1.1 |
$22$ |
$( x^{2} + 6 x + 3 )^{11} + 7$ |
$7$ |
$2$ |
$11$ |
$20$ |
$F_{11}$ (as 22T4) |
$10$ |
$11$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{11}^{10}$ |
$[\ ]_{11}^{10}$ |
$[\ ]^{5}$ |
$[\ ]^{5}$ |
$2$ |
$t^{2} + 6 t + 3$ |
$x^{11} + 7$ |
$[0]$ |
$[5]$ |
$z^{10} + 4 z^9 + 6 z^8 + 4 z^7 + z^6 + z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 7.1.22.21a1.1 |
$22$ |
$x^{22} + 7$ |
$7$ |
$1$ |
$22$ |
$21$ |
$C_2\times F_{11}$ (as 22T6) |
$10$ |
$22$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{22}^{10}$ |
$[\ ]_{22}^{10}$ |
$[\ ]^{10}$ |
$[\ ]^{10}$ |
$2$ |
$t + 4$ |
$x^{22} + 7$ |
$[0]$ |
$[10]$ |
$z^{21} + z^{20} + 3 z^{14} + 3 z^{13} + 3 z^7 + 3 z^6 + 1$ |
undefined |
| 7.1.22.21a1.2 |
$22$ |
$x^{22} + 21$ |
$7$ |
$1$ |
$22$ |
$21$ |
$C_2\times F_{11}$ (as 22T6) |
$10$ |
$22$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{22}^{10}$ |
$[\ ]_{22}^{10}$ |
$[\ ]^{10}$ |
$[\ ]^{10}$ |
$2$ |
$t + 4$ |
$x^{22} + 21$ |
$[0]$ |
$[10]$ |
$z^{21} + z^{20} + 3 z^{14} + 3 z^{13} + 3 z^7 + 3 z^6 + 1$ |
undefined |
