| Label |
Packet size |
Polynomial |
Galois group |
Galois degree |
$\#\Aut(K/\Q_p)$ |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 5.1.20.27a1.1 |
|
$x^{20} + 15 x^{8} + 5$ |
$C_5:C_4$ (as 20T2) |
$20$ |
$20$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
$[1, 13]$ |
| 5.1.20.27a1.2 |
|
$x^{20} + 5 x^{10} + 15 x^{8} + 5$ |
not computed |
$ $not computed$ $ |
$10$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
$[1, 13]$ |
| 5.1.20.27a1.3 |
|
$x^{20} + 10 x^{10} + 15 x^{8} + 5$ |
not computed |
$ $not computed$ $ |
$10$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
$[1, 13]$ |
| 5.1.20.27a1.4 |
|
$x^{20} + 5 x^{9} + 15 x^{8} + 5$ |
$C_5:F_5$ (as 20T26) |
$100$ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
$[1, 13]$ |
| 5.1.20.27a1.5 |
|
$x^{20} + 5 x^{10} + 5 x^{9} + 15 x^{8} + 5$ |
$C_5^2:C_{20}$ (as 20T127) |
$500$ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
$[1, 13]$ |
| 5.1.20.27a1.6 |
|
$x^{20} + 10 x^{10} + 5 x^{9} + 15 x^{8} + 5$ |
$C_5^2:C_{20}$ (as 20T127) |
$500$ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
$[1, 13]$ |
| 5.1.20.27a1.7 |
|
$x^{20} + 15 x^{10} + 5 x^{9} + 15 x^{8} + 5$ |
$C_5^2:C_{20}$ (as 20T127) |
$500$ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
$[1, 13]$ |
| 5.1.20.27a1.8 |
|
$x^{20} + 20 x^{10} + 5 x^{9} + 15 x^{8} + 5$ |
not computed |
$ $not computed$ $ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
$[1, 13]$ |
| 5.1.20.27a1.9 |
|
$x^{20} + 5 x^{8} + 10$ |
$C_5:C_4$ (as 20T2) |
$20$ |
$20$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.10 |
|
$x^{20} + 5 x^{10} + 5 x^{8} + 10$ |
not computed |
$ $not computed$ $ |
$10$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.11 |
|
$x^{20} + 10 x^{10} + 5 x^{8} + 10$ |
$C_5:C_{20}$ (as 20T25) |
$100$ |
$10$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.12 |
|
$x^{20} + 5 x^{9} + 5 x^{8} + 10$ |
not computed |
$ $not computed$ $ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.13 |
|
$x^{20} + 5 x^{10} + 5 x^{9} + 5 x^{8} + 10$ |
$C_5^2:C_{20}$ (as 20T127) |
$500$ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.14 |
|
$x^{20} + 10 x^{10} + 5 x^{9} + 5 x^{8} + 10$ |
not computed |
$ $not computed$ $ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.15 |
|
$x^{20} + 15 x^{10} + 5 x^{9} + 5 x^{8} + 10$ |
$C_5^2:C_{20}$ (as 20T127) |
$500$ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.16 |
|
$x^{20} + 20 x^{10} + 5 x^{9} + 5 x^{8} + 10$ |
$C_5^2:C_{20}$ (as 20T127) |
$500$ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.17 |
|
$x^{20} + 20 x^{8} + 15$ |
not computed |
$ $not computed$ $ |
$20$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.18 |
|
$x^{20} + 5 x^{10} + 20 x^{8} + 15$ |
not computed |
$ $not computed$ $ |
$10$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.19 |
|
$x^{20} + 10 x^{10} + 20 x^{8} + 15$ |
$C_5:C_{20}$ (as 20T25) |
$100$ |
$10$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.20 |
|
$x^{20} + 5 x^{9} + 20 x^{8} + 15$ |
not computed |
$ $not computed$ $ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.21 |
|
$x^{20} + 5 x^{10} + 5 x^{9} + 20 x^{8} + 15$ |
not computed |
$ $not computed$ $ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.22 |
|
$x^{20} + 10 x^{10} + 5 x^{9} + 20 x^{8} + 15$ |
$C_5^2:C_{20}$ (as 20T127) |
$500$ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.23 |
|
$x^{20} + 15 x^{10} + 5 x^{9} + 20 x^{8} + 15$ |
$C_5^2:C_{20}$ (as 20T127) |
$500$ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.24 |
|
$x^{20} + 20 x^{10} + 5 x^{9} + 20 x^{8} + 15$ |
not computed |
$ $not computed$ $ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.25 |
|
$x^{20} + 10 x^{8} + 20$ |
not computed |
$ $not computed$ $ |
$20$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.26 |
|
$x^{20} + 5 x^{10} + 10 x^{8} + 20$ |
$C_5:C_{20}$ (as 20T25) |
$100$ |
$10$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.27 |
|
$x^{20} + 10 x^{10} + 10 x^{8} + 20$ |
$C_5:C_{20}$ (as 20T25) |
$100$ |
$10$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.28 |
|
$x^{20} + 5 x^{9} + 10 x^{8} + 20$ |
not computed |
$ $not computed$ $ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.29 |
|
$x^{20} + 5 x^{10} + 5 x^{9} + 10 x^{8} + 20$ |
not computed |
$ $not computed$ $ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.30 |
|
$x^{20} + 10 x^{10} + 5 x^{9} + 10 x^{8} + 20$ |
not computed |
$ $not computed$ $ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.31 |
|
$x^{20} + 15 x^{10} + 5 x^{9} + 10 x^{8} + 20$ |
not computed |
$ $not computed$ $ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a1.32 |
|
$x^{20} + 20 x^{10} + 5 x^{9} + 10 x^{8} + 20$ |
$C_5^2:C_{20}$ (as 20T127) |
$500$ |
$5$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 1$ |
undefined |
| 5.1.20.27a2.1 |
|
$x^{20} + 5 x^{8} + 5$ |
$C_4\times F_5$ (as 20T20) |
$80$ |
$4$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 2$ |
$[1, 13]$ |
| 5.1.20.27a2.2 |
|
$x^{20} + 5 x^{9} + 5 x^{8} + 5$ |
$F_5^2$ (as 20T102) |
$400$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 2$ |
$[1, 13]$ |
| 5.1.20.27a2.3 |
|
$x^{20} + 10 x^{8} + 10$ |
$C_4\times F_5$ (as 20T20) |
$80$ |
$4$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 2$ |
undefined |
| 5.1.20.27a2.4 |
|
$x^{20} + 5 x^{9} + 10 x^{8} + 10$ |
$F_5^2$ (as 20T102) |
$400$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 2$ |
undefined |
| 5.1.20.27a2.5 |
|
$x^{20} + 15 x^{8} + 15$ |
$C_4\times F_5$ (as 20T20) |
$80$ |
$4$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 2$ |
undefined |
| 5.1.20.27a2.6 |
|
$x^{20} + 5 x^{9} + 15 x^{8} + 15$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 2$ |
undefined |
| 5.1.20.27a2.7 |
|
$x^{20} + 20 x^{8} + 20$ |
$C_4\times F_5$ (as 20T20) |
$80$ |
$4$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 2$ |
undefined |
| 5.1.20.27a2.8 |
|
$x^{20} + 5 x^{9} + 20 x^{8} + 20$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 2$ |
undefined |
| 5.1.20.27a3.1 |
|
$x^{20} + 20 x^{8} + 5$ |
$C_4\times F_5$ (as 20T20) |
$80$ |
$4$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
$[1, 13]$ |
| 5.1.20.27a3.2 |
|
$x^{20} + 5 x^{9} + 20 x^{8} + 5$ |
$F_5^2$ (as 20T102) |
$400$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
$[1, 13]$ |
| 5.1.20.27a3.3 |
|
$x^{20} + 15 x^{8} + 10$ |
$C_4\times F_5$ (as 20T20) |
$80$ |
$4$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.27a3.4 |
|
$x^{20} + 5 x^{9} + 15 x^{8} + 10$ |
$F_5^2$ (as 20T102) |
$400$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.27a3.5 |
|
$x^{20} + 10 x^{8} + 15$ |
$C_4\times F_5$ (as 20T20) |
$80$ |
$4$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.27a3.6 |
|
$x^{20} + 5 x^{9} + 10 x^{8} + 15$ |
$F_5^2$ (as 20T102) |
$400$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.27a3.7 |
|
$x^{20} + 5 x^{8} + 20$ |
$C_4\times F_5$ (as 20T20) |
$80$ |
$4$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.27a3.8 |
|
$x^{20} + 5 x^{9} + 5 x^{8} + 20$ |
$F_5^2$ (as 20T102) |
$400$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.27a4.1 |
|
$x^{20} + 10 x^{8} + 5$ |
not computed |
$ $not computed$ $ |
$4$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 2]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 4$ |
$[1, 13]$ |
| 5.1.20.27a4.2 |
|
$x^{20} + 5 x^{9} + 10 x^{8} + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[8, 0]$ |
$[1, 2]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 4$ |
$[1, 13]$ |
