| 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 |
| 3.3.7.18a1.1 |
$21$ |
$( x^{3} + 2 x + 1 )^{7} + 3$ |
$3$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[\ ]$ |
$[\ ]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{7} + 3$ |
$[0]$ |
$[2]$ |
$z^6 + z^5 + 2 z^3 + 2 z^2 + 1$ |
undefined |
| 5.3.7.18a1.1 |
$21$ |
$( x^{3} + 3 x + 3 )^{7} + 5$ |
$5$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + 3 t + 3$ |
$x^{7} + 5$ |
$[0]$ |
$[2]$ |
$z^6 + 2 z^5 + z^4 + z + 2$ |
undefined |
| 7.3.7.27a2.1 |
$21$ |
$( x^{3} + 6 x^{2} + 4 )^{7} + 28 ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$7$ |
$3$ |
$7$ |
$27$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{7} + 28 x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
$z^3 + (2 t^2 + 5 t + 2)$ |
undefined |
| 7.3.7.27a3.1 |
$21$ |
$( x^{3} + 6 x^{2} + 4 )^{7} + 42 ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$7$ |
$3$ |
$7$ |
$27$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{7} + 42 x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
$z^3 + (3 t^2 + 4 t + 3)$ |
undefined |
| 7.3.7.27a4.1 |
$21$ |
$( x^{3} + 6 x^{2} + 4 )^{7} + 7 ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$7$ |
$3$ |
$7$ |
$27$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{7} + 7 x^{3} + 7$ |
$[3, 0]$ |
$[1]$ |
$z^3 + (4 t^2 + 3 t + 4)$ |
undefined |
| 7.3.7.36a2.1 |
$21$ |
$( x^{3} + 6 x^{2} + 4 )^{7} + 14 ( x^{3} + 6 x^{2} + 4 )^{6} + 7$ |
$7$ |
$3$ |
$7$ |
$36$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t^{3} + 6 t^{2} + 4$ |
$x^{7} + 14 x^{6} + 7$ |
$[6, 0]$ |
$[2]$ |
$z^6 + (4 t^2 + 2 t + 3)$ |
undefined |
| 7.1.21.23a3.1 |
$21$ |
$x^{21} + 7 x^{3} + 7$ |
$7$ |
$1$ |
$21$ |
$23$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t + 4$ |
$x^{21} + 7 x^{3} + 7$ |
$[3, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.23a3.3 |
$21$ |
$x^{21} + 14 x^{3} + 14$ |
$7$ |
$1$ |
$21$ |
$23$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t + 4$ |
$x^{21} + 14 x^{3} + 14$ |
$[3, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.23a3.5 |
$21$ |
$x^{21} + 21 x^{3} + 21$ |
$7$ |
$1$ |
$21$ |
$23$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[\frac{7}{6}]$ |
$[\frac{1}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t + 4$ |
$x^{21} + 21 x^{3} + 21$ |
$[3, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.26a3.3 |
$21$ |
$x^{21} + 14 x^{6} + 21$ |
$7$ |
$1$ |
$21$ |
$26$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[\frac{4}{3}]$ |
$[\frac{1}{3}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t + 4$ |
$x^{21} + 14 x^{6} + 21$ |
$[6, 0]$ |
$[1, 2]$ |
$z^{14} + 3 z^7 + 3,3 z^6 + 3$ |
undefined |
| 7.1.21.32a3.4 |
$21$ |
$x^{21} + 21 x^{12} + 14$ |
$7$ |
$1$ |
$21$ |
$32$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[\frac{5}{3}]$ |
$[\frac{2}{3}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t + 4$ |
$x^{21} + 21 x^{12} + 14$ |
$[12, 0]$ |
$[1, 2]$ |
$z^{14} + 3 z^7 + 3,3 z^6 + 3$ |
undefined |
| 7.1.21.35a3.1 |
$21$ |
$x^{21} + 21 x^{15} + 7$ |
$7$ |
$1$ |
$21$ |
$35$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t + 4$ |
$x^{21} + 21 x^{15} + 7$ |
$[15, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.35a3.52 |
$21$ |
$x^{21} + 42 x^{15} + 14$ |
$7$ |
$1$ |
$21$ |
$35$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t + 4$ |
$x^{21} + 42 x^{15} + 14$ |
$[15, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.41a3.1 |
$21$ |
$x^{21} + 7$ |
$7$ |
$1$ |
$21$ |
$41$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t + 4$ |
$x^{21} + 7$ |
$[21, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.41a3.5 |
$21$ |
$x^{21} + 196 x^{3} + 7$ |
$7$ |
$1$ |
$21$ |
$41$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t + 4$ |
$x^{21} + 196 x^{3} + 7$ |
$[21, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 7.1.21.41a3.6 |
$21$ |
$x^{21} + 245 x^{3} + 7$ |
$7$ |
$1$ |
$21$ |
$41$ |
$F_7$ (as 21T4) |
not computed |
not computed |
$[\frac{13}{6}]$ |
$[\frac{7}{6}]$ |
not computed |
not computed |
not computed |
not computed |
$3$ |
$t + 4$ |
$x^{21} + 245 x^{3} + 7$ |
$[21, 0]$ |
$[1, 1]$ |
$z^{14} + 3 z^7 + 3,3 z^3 + 4$ |
undefined |
| 17.3.7.18a1.1 |
$21$ |
$( x^{3} + x + 14 )^{7} + 17$ |
$17$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + t + 14$ |
$x^{7} + 17$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 4 z^4 + z^3 + z^2 + 4 z + 7$ |
undefined |
| 19.3.7.18a1.1 |
$21$ |
$( x^{3} + 4 x + 17 )^{7} + 19$ |
$19$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + 4 t + 17$ |
$x^{7} + 19$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 2 z^4 + 16 z^3 + 16 z^2 + 2 z + 7$ |
undefined |
| 31.3.7.18a1.1 |
$21$ |
$( x^{3} + x + 28 )^{7} + 31$ |
$31$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + t + 28$ |
$x^{7} + 31$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 21 z^4 + 4 z^3 + 4 z^2 + 21 z + 7$ |
undefined |
| 47.3.7.18a1.1 |
$21$ |
$( x^{3} + 3 x + 42 )^{7} + 47$ |
$47$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + 3 t + 42$ |
$x^{7} + 47$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ |
undefined |
| 59.3.7.18a1.1 |
$21$ |
$( x^{3} + 5 x + 57 )^{7} + 59$ |
$59$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + 5 t + 57$ |
$x^{7} + 59$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ |
undefined |
| 61.3.7.18a1.1 |
$21$ |
$( x^{3} + 7 x + 59 )^{7} + 61$ |
$61$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + 7 t + 59$ |
$x^{7} + 61$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ |
undefined |
| 73.3.7.18a1.1 |
$21$ |
$( x^{3} + 2 x + 68 )^{7} + 73$ |
$73$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + 2 t + 68$ |
$x^{7} + 73$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ |
undefined |
| 89.3.7.18a1.1 |
$21$ |
$( x^{3} + 3 x + 86 )^{7} + 89$ |
$89$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + 3 t + 86$ |
$x^{7} + 89$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ |
undefined |
| 101.3.7.18a1.1 |
$21$ |
$( x^{3} + 3 x + 99 )^{7} + 101$ |
$101$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + 3 t + 99$ |
$x^{7} + 101$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ |
undefined |
| 103.3.7.18a1.1 |
$21$ |
$( x^{3} + 2 x + 98 )^{7} + 103$ |
$103$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + 2 t + 98$ |
$x^{7} + 103$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ |
undefined |
| 131.3.7.18a1.1 |
$21$ |
$( x^{3} + 3 x + 129 )^{7} + 131$ |
$131$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + 3 t + 129$ |
$x^{7} + 131$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ |
undefined |
| 157.3.7.18a1.1 |
$21$ |
$( x^{3} + x + 152 )^{7} + 157$ |
$157$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + t + 152$ |
$x^{7} + 157$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ |
undefined |
| 173.3.7.18a1.1 |
$21$ |
$( x^{3} + 2 x + 171 )^{7} + 173$ |
$173$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + 2 t + 171$ |
$x^{7} + 173$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ |
undefined |
| 199.3.7.18a1.1 |
$21$ |
$( x^{3} + x + 196 )^{7} + 199$ |
$199$ |
$3$ |
$7$ |
$18$ |
$F_7$ (as 21T4) |
$6$ |
$7$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{7}^{6}$ |
$[\ ]_{7}^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + t + 196$ |
$x^{7} + 199$ |
$[0]$ |
$[2]$ |
$z^6 + 7 z^5 + 21 z^4 + 35 z^3 + 35 z^2 + 21 z + 7$ |
undefined |
