| 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 |
| 7.3.7.27a33.1 |
$21$ |
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 28 x + 42\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$7$ |
$3$ |
$7$ |
$27$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{7} + \left(14 t^{2} + 28 t + 42\right) x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
$z^3 + (4 t^2 + 2 t + 2)$ |
undefined |
| 7.3.7.27a57.1 |
$21$ |
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(28 x^{2} + 35 x + 21\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$7$ |
$3$ |
$7$ |
$27$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{7} + \left(35 t^{2} + 14\right) x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
$z^3 + 2$ |
undefined |
| 7.3.7.27a78.1 |
$21$ |
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(7 x^{2} + 14 x + 21\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$7$ |
$3$ |
$7$ |
$27$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{7} + \left(7 t^{2} + 14 t + 21\right) x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
$z^3 + (2 t^2 + t + 1)$ |
undefined |
| 7.1.21.29a3.11 |
$21$ |
$x^{21} + 7 x^{10} + 28 x^{9} + 14$ |
$7$ |
$1$ |
$21$ |
$29$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 7 x^{10} + 28 x^{9} + 14$ |
$[9, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 3$ |
undefined |
| 7.1.21.29a3.15 |
$21$ |
$x^{21} + 21 x^{10} + 7 x^{9} + 21$ |
$7$ |
$1$ |
$21$ |
$29$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 21 x^{10} + 7 x^{9} + 21$ |
$[9, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.29a3.17 |
$21$ |
$x^{21} + 7 x^{10} + 42 x^{9} + 21$ |
$7$ |
$1$ |
$21$ |
$29$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 7 x^{10} + 42 x^{9} + 21$ |
$[9, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 3$ |
undefined |
| 7.1.21.35a3.4 |
$21$ |
$x^{21} + 7 x^{16} + 21 x^{15} + 7$ |
$7$ |
$1$ |
$21$ |
$35$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 7 x^{16} + 21 x^{15} + 7$ |
$[15, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.35a3.11 |
$21$ |
$x^{21} + 21 x^{16} + 21 x^{15} + 7$ |
$7$ |
$1$ |
$21$ |
$35$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 21 x^{16} + 21 x^{15} + 7$ |
$[15, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.35a3.21 |
$21$ |
$x^{21} + 7 x^{16} + 28 x^{15} + 7$ |
$7$ |
$1$ |
$21$ |
$35$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 7 x^{16} + 28 x^{15} + 7$ |
$[15, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 3$ |
undefined |
| 7.1.21.35a3.38 |
$21$ |
$x^{21} + 7 x^{16} + 7 x^{15} + 14$ |
$7$ |
$1$ |
$21$ |
$35$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 7 x^{16} + 7 x^{15} + 14$ |
$[15, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 3$ |
undefined |
| 7.1.21.35a3.45 |
$21$ |
$x^{21} + 21 x^{16} + 7 x^{15} + 14$ |
$7$ |
$1$ |
$21$ |
$35$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 21 x^{16} + 7 x^{15} + 14$ |
$[15, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 3$ |
undefined |
| 7.1.21.35a3.55 |
$21$ |
$x^{21} + 7 x^{16} + 42 x^{15} + 14$ |
$7$ |
$1$ |
$21$ |
$35$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 7 x^{16} + 42 x^{15} + 14$ |
$[15, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.35a3.62 |
$21$ |
$x^{21} + 21 x^{16} + 42 x^{15} + 14$ |
$7$ |
$1$ |
$21$ |
$35$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 21 x^{16} + 42 x^{15} + 14$ |
$[15, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.35a3.96 |
$21$ |
$x^{21} + 21 x^{16} + 35 x^{15} + 21$ |
$7$ |
$1$ |
$21$ |
$35$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 21 x^{16} + 35 x^{15} + 21$ |
$[15, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 3$ |
undefined |
| 7.1.21.38a3.2 |
$21$ |
$x^{21} + 7 x^{20} + 7 x^{18} + 7$ |
$7$ |
$1$ |
$21$ |
$38$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 7 x^{20} + 7 x^{18} + 7$ |
$[18, 0]$ |
$[1, 2]$ |
$z^{14} + 3 z^7 + 3,3 z^6 + 3$ |
undefined |
| 7.1.21.38a3.4 |
$21$ |
$x^{21} + 7 x^{19} + 7 x^{18} + 7$ |
$7$ |
$1$ |
$21$ |
$38$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 7 x^{19} + 7 x^{18} + 7$ |
$[18, 0]$ |
$[1, 2]$ |
$z^{14} + 3 z^7 + 3,3 z^6 + 3$ |
undefined |
| 7.1.21.38a3.11 |
$21$ |
$x^{21} + 21 x^{19} + 7 x^{18} + 7$ |
$7$ |
$1$ |
$21$ |
$38$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 21 x^{19} + 7 x^{18} + 7$ |
$[18, 0]$ |
$[1, 2]$ |
$z^{14} + 3 z^7 + 3,3 z^6 + 3$ |
undefined |
| 7.1.21.38a3.19 |
$21$ |
$x^{21} + 7 x^{20} + 14 x^{18} + 14$ |
$7$ |
$1$ |
$21$ |
$38$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 7 x^{20} + 14 x^{18} + 14$ |
$[18, 0]$ |
$[1, 2]$ |
$z^{14} + 3 z^7 + 3,3 z^6 + 3$ |
undefined |
| 7.1.21.38a3.21 |
$21$ |
$x^{21} + 7 x^{19} + 14 x^{18} + 14$ |
$7$ |
$1$ |
$21$ |
$38$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 7 x^{19} + 14 x^{18} + 14$ |
$[18, 0]$ |
$[1, 2]$ |
$z^{14} + 3 z^7 + 3,3 z^6 + 3$ |
undefined |
| 7.1.21.38a3.28 |
$21$ |
$x^{21} + 21 x^{19} + 14 x^{18} + 14$ |
$7$ |
$1$ |
$21$ |
$38$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 21 x^{19} + 14 x^{18} + 14$ |
$[18, 0]$ |
$[1, 2]$ |
$z^{14} + 3 z^7 + 3,3 z^6 + 3$ |
undefined |
| 7.1.21.38a3.37 |
$21$ |
$x^{21} + 21 x^{20} + 21 x^{18} + 21$ |
$7$ |
$1$ |
$21$ |
$38$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 21 x^{20} + 21 x^{18} + 21$ |
$[18, 0]$ |
$[1, 2]$ |
$z^{14} + 3 z^7 + 3,3 z^6 + 3$ |
undefined |
| 7.1.21.38a3.45 |
$21$ |
$x^{21} + 21 x^{19} + 21 x^{18} + 21$ |
$7$ |
$1$ |
$21$ |
$38$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 21 x^{19} + 21 x^{18} + 21$ |
$[18, 0]$ |
$[1, 2]$ |
$z^{14} + 3 z^7 + 3,3 z^6 + 3$ |
undefined |
| 7.1.21.41a3.8 |
$21$ |
$x^{21} + 49 x^{2} + 7$ |
$7$ |
$1$ |
$21$ |
$41$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 49 x^{2} + 7$ |
$[21, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.41a3.11 |
$21$ |
$x^{21} + 147 x^{3} + 49 x^{2} + 7$ |
$7$ |
$1$ |
$21$ |
$41$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 147 x^{3} + 49 x^{2} + 7$ |
$[21, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.41a3.12 |
$21$ |
$x^{21} + 196 x^{3} + 49 x^{2} + 7$ |
$7$ |
$1$ |
$21$ |
$41$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 196 x^{3} + 49 x^{2} + 7$ |
$[21, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.41a3.13 |
$21$ |
$x^{21} + 245 x^{3} + 49 x^{2} + 7$ |
$7$ |
$1$ |
$21$ |
$41$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 245 x^{3} + 49 x^{2} + 7$ |
$[21, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.41a3.15 |
$21$ |
$x^{21} + 147 x^{2} + 7$ |
$7$ |
$1$ |
$21$ |
$41$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 147 x^{2} + 7$ |
$[21, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.41a3.16 |
$21$ |
$x^{21} + 49 x^{3} + 147 x^{2} + 7$ |
$7$ |
$1$ |
$21$ |
$41$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 49 x^{3} + 147 x^{2} + 7$ |
$[21, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.41a3.19 |
$21$ |
$x^{21} + 196 x^{3} + 147 x^{2} + 7$ |
$7$ |
$1$ |
$21$ |
$41$ |
$C_7:F_7$ (as 21T16) |
not computed |
not computed |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 4$ |
$x^{21} + 196 x^{3} + 147 x^{2} + 7$ |
$[21, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
