These invariants are all associated to absolute extensions of $\Q_{ 5 }$ within this relative family, not the relative extension.
| Label |
Polynomial $/ \Q_p$ |
Galois group $/ \Q_p$ |
Galois degree $/ \Q_p$ |
$\#\Aut(K/\Q_p)$ |
Artin slope content $/ \Q_p$ |
Swan slope content $/ \Q_p$ |
Hidden Artin slopes $/ \Q_p$ |
Hidden Swan slopes $/ \Q_p$ |
Ind. of Insep. $/ \Q_p$ |
Assoc. Inertia $/ \Q_p$ |
Resid. Poly |
Jump Set |
| 5.1.20.39a3.1 |
$x^{20} + 10$ |
not computed |
$ $not computed$ $ |
$4$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.2 |
$x^{20} + 25 x^{4} + 10$ |
$C_4\times F_5$ (as 20T20) |
$80$ |
$4$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.3 |
$x^{20} + 50 x^{4} + 10$ |
not computed |
$ $not computed$ $ |
$4$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.4 |
$x^{20} + 75 x^{4} + 10$ |
$C_4\times F_5$ (as 20T20) |
$80$ |
$4$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.5 |
$x^{20} + 100 x^{4} + 10$ |
not computed |
$ $not computed$ $ |
$4$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.6 |
$x^{20} + 25 x^{3} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.7 |
$x^{20} + 25 x^{4} + 25 x^{3} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.8 |
$x^{20} + 50 x^{4} + 25 x^{3} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.9 |
$x^{20} + 75 x^{4} + 25 x^{3} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.10 |
$x^{20} + 100 x^{4} + 25 x^{3} + 10$ |
$F_5^2$ (as 20T102) |
$400$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.11 |
$x^{20} + 25 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.12 |
$x^{20} + 25 x^{4} + 25 x^{2} + 10$ |
$C_5^2:C_4^2$ (as 20T91) |
$400$ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.13 |
$x^{20} + 50 x^{4} + 25 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.14 |
$x^{20} + 75 x^{4} + 25 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.15 |
$x^{20} + 100 x^{4} + 25 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.16 |
$x^{20} + 25 x^{3} + 25 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.17 |
$x^{20} + 25 x^{4} + 25 x^{3} + 25 x^{2} + 10$ |
$C_5:F_5^2$ (as 20T232) |
$2000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.18 |
$x^{20} + 50 x^{4} + 25 x^{3} + 25 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.19 |
$x^{20} + 75 x^{4} + 25 x^{3} + 25 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.20 |
$x^{20} + 100 x^{4} + 25 x^{3} + 25 x^{2} + 10$ |
$C_5:F_5^2$ (as 20T232) |
$2000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.21 |
$x^{20} + 50 x^{3} + 25 x^{2} + 10$ |
$C_5:F_5^2$ (as 20T232) |
$2000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.22 |
$x^{20} + 25 x^{4} + 50 x^{3} + 25 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.23 |
$x^{20} + 50 x^{4} + 50 x^{3} + 25 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.24 |
$x^{20} + 75 x^{4} + 50 x^{3} + 25 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.25 |
$x^{20} + 100 x^{4} + 50 x^{3} + 25 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.26 |
$x^{20} + 50 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.27 |
$x^{20} + 25 x^{4} + 50 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.28 |
$x^{20} + 50 x^{4} + 50 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.29 |
$x^{20} + 75 x^{4} + 50 x^{2} + 10$ |
$C_5^2:C_4^2$ (as 20T91) |
$400$ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.30 |
$x^{20} + 100 x^{4} + 50 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$2$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.31 |
$x^{20} + 25 x^{3} + 50 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.32 |
$x^{20} + 25 x^{4} + 25 x^{3} + 50 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.33 |
$x^{20} + 50 x^{4} + 25 x^{3} + 50 x^{2} + 10$ |
$C_5:F_5^2$ (as 20T232) |
$2000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.34 |
$x^{20} + 75 x^{4} + 25 x^{3} + 50 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.35 |
$x^{20} + 100 x^{4} + 25 x^{3} + 50 x^{2} + 10$ |
$C_5:F_5^2$ (as 20T232) |
$2000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.36 |
$x^{20} + 50 x^{3} + 50 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.37 |
$x^{20} + 25 x^{4} + 50 x^{3} + 50 x^{2} + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.38 |
$x^{20} + 50 x^{4} + 50 x^{3} + 50 x^{2} + 10$ |
$C_5:F_5^2$ (as 20T232) |
$2000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.39 |
$x^{20} + 75 x^{4} + 50 x^{3} + 50 x^{2} + 10$ |
$C_5:F_5^2$ (as 20T232) |
$2000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.40 |
$x^{20} + 100 x^{4} + 50 x^{3} + 50 x^{2} + 10$ |
$C_5:F_5^2$ (as 20T232) |
$2000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.41 |
$x^{20} + 25 x + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.42 |
$x^{20} + 25 x^{4} + 25 x + 10$ |
$F_5^2$ (as 20T102) |
$400$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.43 |
$x^{20} + 50 x^{4} + 25 x + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.44 |
$x^{20} + 75 x^{4} + 25 x + 10$ |
$F_5^2$ (as 20T102) |
$400$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.45 |
$x^{20} + 100 x^{4} + 25 x + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.46 |
$x^{20} + 25 x^{3} + 25 x + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.47 |
$x^{20} + 25 x^{4} + 25 x^{3} + 25 x + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.48 |
$x^{20} + 50 x^{4} + 25 x^{3} + 25 x + 10$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.49 |
$x^{20} + 75 x^{4} + 25 x^{3} + 25 x + 10$ |
$C_5:F_5^2$ (as 20T232) |
$2000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
| 5.1.20.39a3.50 |
$x^{20} + 100 x^{4} + 25 x^{3} + 25 x + 10$ |
$C_5:F_5^2$ (as 20T232) |
$2000$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[20, 0]$ |
$[1, 4]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 3$ |
undefined |
