| 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 |
| 3.4.3.12a14.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{3} + 6 x^{2} + 3\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_2\times C_3^2:C_4$ (as 12T41) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$2$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + t^2 + 2 t + 2)$ |
undefined |
| 3.4.3.12a21.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{3} + 3 x^{2} + 6\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_2\times C_3^2:C_4$ (as 12T41) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$2$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^3 + 2 t^2 + t + 1)$ |
undefined |
| 3.2.6.18a3.4 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + \left(6 x + 3\right) ( x^{2} + 2 x + 2 )^{5} + \left(6 x + 6\right) ( x^{2} + 2 x + 2 )^{4} + \left(6 x + 6\right) ( x^{2} + 2 x + 2 ) + 3 x$ |
$3$ |
$2$ |
$6$ |
$18$ |
$C_2\times C_3^2:C_4$ (as 12T41) |
$4$ |
$2$ |
$[2]$ |
$[1]$ |
$[2, 2]_{2}^{4}$ |
$[1,1]_{2}^{4}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$2$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(6 t + 6\right) x^{4} + 3 t$ |
$[4, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + t$ |
undefined |
| 3.2.6.18a6.4 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + \left(6 x + 3\right) ( x^{2} + 2 x + 2 )^{5} + 3 ( x^{2} + 2 x + 2 )^{4} + \left(6 x + 6\right) ( x^{2} + 2 x + 2 ) + 3 x$ |
$3$ |
$2$ |
$6$ |
$18$ |
$C_2\times C_3^2:C_4$ (as 12T41) |
$4$ |
$2$ |
$[2]$ |
$[1]$ |
$[2, 2]_{2}^{4}$ |
$[1,1]_{2}^{4}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$2$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 3 x^{4} + 3 t$ |
$[4, 0]$ |
$[1, 2]$ |
$z^3 + 2,2 z^2 + (2 t + 1)$ |
undefined |
