| 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 |
| 2.4.4.44a1.135 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_{16} : C_2$ (as 16T22) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{4}$ |
$[1,2,3]^{4}$ |
$[2]$ |
$[1]$ |
$8$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 8 x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.137 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_{16} : C_2$ (as 16T22) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{8}$ |
$[2,3]^{8}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$8$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x^{3} + 8 x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.140 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_{16} : C_2$ (as 16T22) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{4}$ |
$[1,2,3]^{4}$ |
$[2]$ |
$[1]$ |
$8$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 8 x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.142 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_{16} : C_2$ (as 16T22) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{8}$ |
$[2,3]^{8}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$8$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + 8 x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1247 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_{16} : C_2$ (as 16T22) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{4}$ |
$[1,2,3]^{4}$ |
$[2]$ |
$[1]$ |
$8$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 x^{2} + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1248 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 24 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_{16} : C_2$ (as 16T22) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{4}$ |
$[1,2,3]^{4}$ |
$[2]$ |
$[1]$ |
$8$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 x^{2} + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
