| 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 |
| 5.4.5.32a49.3 |
$20$ |
$( x^{4} + 4 x^{2} + 4 x + 2 )^{5} + \left(5 x^{3} + 5 x^{2} + 5 x + 5\right) ( x^{4} + 4 x^{2} + 4 x + 2 )^{4} + 100 x + 5$ |
$5$ |
$4$ |
$5$ |
$32$ |
$C_5:F_5$ (as 20T27) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$10$ |
$t^{4} + 4 t^{2} + 4 t + 2$ |
$x^{5} + \left(20 t^{3} + 20 t^{2} + 20 t + 5\right) x^{4} + 5$ |
$[4, 0]$ |
$[1]$ |
$z^4 + (4 t^3 + 3 t + 1)$ |
undefined |
| 5.2.10.26a19.3 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + 20 x ( x^{2} + 4 x + 2 )^{5} + \left(15 x + 10\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_5:F_5$ (as 20T27) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$10$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 10\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 1]$ |
$z^5 + 2,2 z^4 + (4 t + 2)$ |
undefined |
| 5.1.20.31a1.6 |
$20$ |
$x^{20} + 10 x^{14} + 10 x^{12} + 5$ |
$5$ |
$1$ |
$20$ |
$31$ |
$C_5:F_5$ (as 20T27) |
not computed |
not computed |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$10$ |
$t + 3$ |
$x^{20} + 10 x^{14} + 10 x^{12} + 5$ |
$[12, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
$[1, 17]$ |
| 5.1.20.31a1.105 |
$20$ |
$x^{20} + 10 x^{14} + 15 x^{12} + 20$ |
$5$ |
$1$ |
$20$ |
$31$ |
$C_5:F_5$ (as 20T27) |
not computed |
not computed |
$[\frac{7}{4}]$ |
$[\frac{3}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$10$ |
$t + 3$ |
$x^{20} + 10 x^{14} + 15 x^{12} + 20$ |
$[12, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.39a1.36 |
$20$ |
$x^{20} + 25 x^{2} + 5$ |
$5$ |
$1$ |
$20$ |
$39$ |
$C_5:F_5$ (as 20T27) |
not computed |
not computed |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$10$ |
$t + 3$ |
$x^{20} + 25 x^{2} + 5$ |
$[20, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
$[1, 21]$ |
| 5.1.20.39a1.113 |
$20$ |
$x^{20} + 100 x^{4} + 50 x^{2} + 5$ |
$5$ |
$1$ |
$20$ |
$39$ |
$C_5:F_5$ (as 20T27) |
not computed |
not computed |
$[\frac{9}{4}]$ |
$[\frac{5}{4}]$ |
not computed |
not computed |
not computed |
not computed |
$10$ |
$t + 3$ |
$x^{20} + 100 x^{4} + 50 x^{2} + 5$ |
$[20, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
$[1, 21]$ |
