| 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 |
| 5.1.20.37a1.1 |
|
$x^{20} + 10 x^{18} + 5$ |
not computed |
$ $not computed$ $ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.2 |
|
$x^{20} + 10 x^{18} + 25 x^{2} + 5$ |
not computed |
$ $not computed$ $ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.3 |
|
$x^{20} + 10 x^{18} + 50 x^{2} + 5$ |
$C_5^2:\OD_{16}$ (as 20T109) |
$400$ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.4 |
|
$x^{20} + 10 x^{18} + 25 x + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.5 |
|
$x^{20} + 10 x^{18} + 25 x^{2} + 25 x + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.6 |
|
$x^{20} + 10 x^{18} + 50 x^{2} + 25 x + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.7 |
|
$x^{20} + 10 x^{18} + 75 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.8 |
|
$x^{20} + 10 x^{18} + 100 x^{2} + 25 x + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.9 |
|
$x^{20} + 5 x^{19} + 10 x^{18} + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.10 |
|
$x^{20} + 5 x^{19} + 10 x^{18} + 25 x^{2} + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.11 |
|
$x^{20} + 5 x^{19} + 10 x^{18} + 50 x^{2} + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.12 |
|
$x^{20} + 5 x^{19} + 10 x^{18} + 25 x + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.13 |
|
$x^{20} + 5 x^{19} + 10 x^{18} + 25 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.14 |
|
$x^{20} + 5 x^{19} + 10 x^{18} + 50 x^{2} + 25 x + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.15 |
|
$x^{20} + 5 x^{19} + 10 x^{18} + 75 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.16 |
|
$x^{20} + 5 x^{19} + 10 x^{18} + 100 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.17 |
|
$x^{20} + 10 x^{19} + 10 x^{18} + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.18 |
|
$x^{20} + 10 x^{19} + 10 x^{18} + 25 x^{2} + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.19 |
|
$x^{20} + 10 x^{19} + 10 x^{18} + 50 x^{2} + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.20 |
|
$x^{20} + 10 x^{19} + 10 x^{18} + 25 x + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.21 |
|
$x^{20} + 10 x^{19} + 10 x^{18} + 25 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.22 |
|
$x^{20} + 10 x^{19} + 10 x^{18} + 50 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.23 |
|
$x^{20} + 10 x^{19} + 10 x^{18} + 75 x^{2} + 25 x + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.24 |
|
$x^{20} + 10 x^{19} + 10 x^{18} + 100 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.25 |
|
$x^{20} + 15 x^{19} + 10 x^{18} + 25 x + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.26 |
|
$x^{20} + 15 x^{19} + 10 x^{18} + 25 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.27 |
|
$x^{20} + 15 x^{19} + 10 x^{18} + 50 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.28 |
|
$x^{20} + 15 x^{19} + 10 x^{18} + 75 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.29 |
|
$x^{20} + 15 x^{19} + 10 x^{18} + 100 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.30 |
|
$x^{20} + 20 x^{19} + 10 x^{18} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.31 |
|
$x^{20} + 20 x^{19} + 10 x^{18} + 25 x^{2} + 25 x + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.32 |
|
$x^{20} + 20 x^{19} + 10 x^{18} + 50 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.33 |
|
$x^{20} + 20 x^{19} + 10 x^{18} + 75 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.34 |
|
$x^{20} + 20 x^{19} + 10 x^{18} + 100 x^{2} + 25 x + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 4$ |
$[1, 21]$ |
| 5.1.20.37a1.35 |
|
$x^{20} + 15 x^{18} + 25 x^{2} + 5$ |
not computed |
$ $not computed$ $ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.36 |
|
$x^{20} + 15 x^{18} + 50 x^{2} + 5$ |
$C_5^2:\OD_{16}$ (as 20T109) |
$400$ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.37 |
|
$x^{20} + 15 x^{18} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.38 |
|
$x^{20} + 15 x^{18} + 25 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.39 |
|
$x^{20} + 15 x^{18} + 50 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.40 |
|
$x^{20} + 15 x^{18} + 75 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.41 |
|
$x^{20} + 15 x^{18} + 100 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.42 |
|
$x^{20} + 5 x^{19} + 15 x^{18} + 25 x^{2} + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.43 |
|
$x^{20} + 5 x^{19} + 15 x^{18} + 50 x^{2} + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.44 |
|
$x^{20} + 5 x^{19} + 15 x^{18} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.45 |
|
$x^{20} + 5 x^{19} + 15 x^{18} + 25 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.46 |
|
$x^{20} + 5 x^{19} + 15 x^{18} + 50 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.47 |
|
$x^{20} + 5 x^{19} + 15 x^{18} + 75 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.48 |
|
$x^{20} + 5 x^{19} + 15 x^{18} + 100 x^{2} + 25 x + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.49 |
|
$x^{20} + 10 x^{19} + 15 x^{18} + 25 x^{2} + 5$ |
$C_5^4.\OD_{16}$ (as 20T386) |
$10000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
| 5.1.20.37a1.50 |
|
$x^{20} + 10 x^{19} + 15 x^{18} + 50 x^{2} + 5$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[18, 0]$ |
$[1, 1]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^2 + 1$ |
$[1, 21]$ |
