| 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 |
| 5.2.10.26a9.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(15 x + 5\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_4\times D_5$ (as 20T6) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(15 t + 5\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^4 + (2 t + 2)$ |
undefined |
| 5.2.10.26a14.1 |
$20$ |
$( x^{2} + 4 x + 2 )^{10} + \left(10 x + 20\right) ( x^{2} + 4 x + 2 )^{4} + \left(20 x + 15\right) ( x^{2} + 4 x + 2 )^{2} + \left(5 x + 10\right) ( x^{2} + 4 x + 2 ) + 5 x$ |
$5$ |
$2$ |
$10$ |
$26$ |
$C_4\times D_5$ (as 20T6) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$4$ |
$t^{2} + 4 t + 2$ |
$x^{10} + \left(10 t + 20\right) x^{4} + 5 t$ |
$[4, 0]$ |
$[1, 2]$ |
$z^5 + 2,2 z^4 + (3 t + 3)$ |
undefined |
| 5.1.20.35a4.1 |
$20$ |
$x^{20} + 5 x^{16} + 5$ |
$5$ |
$1$ |
$20$ |
$35$ |
$C_4\times D_5$ (as 20T6) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$4$ |
$t + 3$ |
$x^{20} + 5 x^{16} + 5$ |
$[16, 0]$ |
$[1, 2]$ |
$z^{15} + 4 z^{10} + z^5 + 4,4 z^4 + 4$ |
$[1, 21]$ |
| 29.1.20.19a1.1 |
$20$ |
$x^{20} + 29$ |
$29$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 27$ |
$x^{20} + 29$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 16 z^{17} + 9 z^{16} + 2 z^{15} + 18 z^{14} + 16 z^{13} + 3 z^{12} + 23 z^{11} + 21 z^{10} + 26 z^9 + 21 z^8 + 23 z^7 + 3 z^6 + 16 z^5 + 18 z^4 + 2 z^3 + 9 z^2 + 16 z + 20$ |
undefined |
| 29.1.20.19a1.2 |
$20$ |
$x^{20} + 58$ |
$29$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 27$ |
$x^{20} + 58$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 16 z^{17} + 9 z^{16} + 2 z^{15} + 18 z^{14} + 16 z^{13} + 3 z^{12} + 23 z^{11} + 21 z^{10} + 26 z^9 + 21 z^8 + 23 z^7 + 3 z^6 + 16 z^5 + 18 z^4 + 2 z^3 + 9 z^2 + 16 z + 20$ |
undefined |
| 29.1.20.19a1.3 |
$20$ |
$x^{20} + 116$ |
$29$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 27$ |
$x^{20} + 116$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 16 z^{17} + 9 z^{16} + 2 z^{15} + 18 z^{14} + 16 z^{13} + 3 z^{12} + 23 z^{11} + 21 z^{10} + 26 z^9 + 21 z^8 + 23 z^7 + 3 z^6 + 16 z^5 + 18 z^4 + 2 z^3 + 9 z^2 + 16 z + 20$ |
undefined |
| 29.1.20.19a1.4 |
$20$ |
$x^{20} + 232$ |
$29$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 27$ |
$x^{20} + 232$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 16 z^{17} + 9 z^{16} + 2 z^{15} + 18 z^{14} + 16 z^{13} + 3 z^{12} + 23 z^{11} + 21 z^{10} + 26 z^9 + 21 z^8 + 23 z^7 + 3 z^6 + 16 z^5 + 18 z^4 + 2 z^3 + 9 z^2 + 16 z + 20$ |
undefined |
| 89.1.20.19a1.1 |
$20$ |
$x^{20} + 89$ |
$89$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 86$ |
$x^{20} + 89$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 12 z^{17} + 72 z^{16} + 39 z^{15} + 18 z^{14} + 45 z^{13} + z^{12} + 35 z^{11} + 17 z^{10} + 81 z^9 + 17 z^8 + 35 z^7 + z^6 + 45 z^5 + 18 z^4 + 39 z^3 + 72 z^2 + 12 z + 20$ |
undefined |
| 89.1.20.19a1.2 |
$20$ |
$x^{20} + 267$ |
$89$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 86$ |
$x^{20} + 267$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 12 z^{17} + 72 z^{16} + 39 z^{15} + 18 z^{14} + 45 z^{13} + z^{12} + 35 z^{11} + 17 z^{10} + 81 z^9 + 17 z^8 + 35 z^7 + z^6 + 45 z^5 + 18 z^4 + 39 z^3 + 72 z^2 + 12 z + 20$ |
undefined |
| 89.1.20.19a1.3 |
$20$ |
$x^{20} + 801$ |
$89$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 86$ |
$x^{20} + 801$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 12 z^{17} + 72 z^{16} + 39 z^{15} + 18 z^{14} + 45 z^{13} + z^{12} + 35 z^{11} + 17 z^{10} + 81 z^9 + 17 z^8 + 35 z^7 + z^6 + 45 z^5 + 18 z^4 + 39 z^3 + 72 z^2 + 12 z + 20$ |
undefined |
| 89.1.20.19a1.4 |
$20$ |
$x^{20} + 2403$ |
$89$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 86$ |
$x^{20} + 2403$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 12 z^{17} + 72 z^{16} + 39 z^{15} + 18 z^{14} + 45 z^{13} + z^{12} + 35 z^{11} + 17 z^{10} + 81 z^9 + 17 z^8 + 35 z^7 + z^6 + 45 z^5 + 18 z^4 + 39 z^3 + 72 z^2 + 12 z + 20$ |
undefined |
| 109.1.20.19a1.1 |
$20$ |
$x^{20} + 109$ |
$109$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 103$ |
$x^{20} + 109$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 81 z^{17} + 50 z^{16} + 49 z^{15} + 26 z^{14} + 65 z^{13} + 21 z^{12} + 75 z^{11} + 100 z^{10} + z^9 + 100 z^8 + 75 z^7 + 21 z^6 + 65 z^5 + 26 z^4 + 49 z^3 + 50 z^2 + 81 z + 20$ |
undefined |
| 109.1.20.19a1.2 |
$20$ |
$x^{20} + 654$ |
$109$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 103$ |
$x^{20} + 654$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 81 z^{17} + 50 z^{16} + 49 z^{15} + 26 z^{14} + 65 z^{13} + 21 z^{12} + 75 z^{11} + 100 z^{10} + z^9 + 100 z^8 + 75 z^7 + 21 z^6 + 65 z^5 + 26 z^4 + 49 z^3 + 50 z^2 + 81 z + 20$ |
undefined |
| 109.1.20.19a1.3 |
$20$ |
$x^{20} + 3924$ |
$109$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 103$ |
$x^{20} + 3924$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 81 z^{17} + 50 z^{16} + 49 z^{15} + 26 z^{14} + 65 z^{13} + 21 z^{12} + 75 z^{11} + 100 z^{10} + z^9 + 100 z^8 + 75 z^7 + 21 z^6 + 65 z^5 + 26 z^4 + 49 z^3 + 50 z^2 + 81 z + 20$ |
undefined |
| 109.1.20.19a1.4 |
$20$ |
$x^{20} + 11663$ |
$109$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 103$ |
$x^{20} + 11663$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 81 z^{17} + 50 z^{16} + 49 z^{15} + 26 z^{14} + 65 z^{13} + 21 z^{12} + 75 z^{11} + 100 z^{10} + z^9 + 100 z^8 + 75 z^7 + 21 z^6 + 65 z^5 + 26 z^4 + 49 z^3 + 50 z^2 + 81 z + 20$ |
undefined |
| 149.1.20.19a1.1 |
$20$ |
$x^{20} + 149$ |
$149$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 147$ |
$x^{20} + 149$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 41 z^{17} + 97 z^{16} + 77 z^{15} + 8 z^{14} + 20 z^{13} + 40 z^{12} + 65 z^{11} + 37 z^{10} + 145 z^9 + 37 z^8 + 65 z^7 + 40 z^6 + 20 z^5 + 8 z^4 + 77 z^3 + 97 z^2 + 41 z + 20$ |
undefined |
| 149.1.20.19a1.2 |
$20$ |
$x^{20} + 298$ |
$149$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 147$ |
$x^{20} + 298$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 41 z^{17} + 97 z^{16} + 77 z^{15} + 8 z^{14} + 20 z^{13} + 40 z^{12} + 65 z^{11} + 37 z^{10} + 145 z^9 + 37 z^8 + 65 z^7 + 40 z^6 + 20 z^5 + 8 z^4 + 77 z^3 + 97 z^2 + 41 z + 20$ |
undefined |
| 149.1.20.19a1.3 |
$20$ |
$x^{20} + 596$ |
$149$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 147$ |
$x^{20} + 596$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 41 z^{17} + 97 z^{16} + 77 z^{15} + 8 z^{14} + 20 z^{13} + 40 z^{12} + 65 z^{11} + 37 z^{10} + 145 z^9 + 37 z^8 + 65 z^7 + 40 z^6 + 20 z^5 + 8 z^4 + 77 z^3 + 97 z^2 + 41 z + 20$ |
undefined |
| 149.1.20.19a1.4 |
$20$ |
$x^{20} + 1192$ |
$149$ |
$1$ |
$20$ |
$19$ |
$C_4\times D_5$ (as 20T6) |
$2$ |
$20$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{20}^{2}$ |
$[\ ]_{20}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 147$ |
$x^{20} + 1192$ |
$[0]$ |
$[2]$ |
$z^{19} + 20 z^{18} + 41 z^{17} + 97 z^{16} + 77 z^{15} + 8 z^{14} + 20 z^{13} + 40 z^{12} + 65 z^{11} + 37 z^{10} + 145 z^9 + 37 z^8 + 65 z^7 + 40 z^6 + 20 z^5 + 8 z^4 + 77 z^3 + 97 z^2 + 41 z + 20$ |
undefined |
