| 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 |
| 7.2.7.22a7.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + 28 x ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(21 t + 28\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + (5 t + 4)$ |
undefined |
| 7.2.7.22a8.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(28 x + 28\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(28 t + 28\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + (t + 6)$ |
undefined |
| 7.2.7.22a9.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(28 x + 14\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$D_7:F_7$ (as 14T24) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(21 t + 42\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + (3 t + 5)$ |
undefined |
| 7.2.7.22a10.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(28 x + 42\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(21 t + 21\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + 6 t$ |
undefined |
| 7.2.7.22a11.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + 7 x ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 7 t x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + (3 t + 1)$ |
undefined |
| 7.2.7.22a12.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(7 x + 28\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$D_7:F_7$ (as 14T24) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(7 t + 28\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + (6 t + 3)$ |
undefined |
| 7.2.7.22a13.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(7 x + 35\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(42 t + 42\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + 5 t$ |
undefined |
| 7.2.7.22a14.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(7 x + 14\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$D_7:F_7$ (as 14T24) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(42 t + 21\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + (t + 2)$ |
undefined |
| 7.2.7.22a15.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(7 x + 21\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$D_7:F_7$ (as 14T24) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(42 t + 28\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + 6$ |
undefined |
| 7.2.7.22a16.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + 35 x ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 35 t x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + (t + 5)$ |
undefined |
| 7.2.7.22a17.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(35 x + 28\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(35 t + 28\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + 4 t$ |
undefined |
| 7.2.7.22a18.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(35 x + 35\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(35 t + 35\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + (3 t + 4)$ |
undefined |
| 7.2.7.22a19.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(35 x + 42\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$D_7:F_7$ (as 14T24) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(35 t + 42\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + (2 t + 1)$ |
undefined |
| 7.2.7.22a20.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + 14 x ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(35 t + 14\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + (6 t + 2)$ |
undefined |
| 7.2.7.22a21.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(14 x + 7\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$D_7:F_7$ (as 14T24) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(14 t + 7\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + (5 t + 6)$ |
undefined |
| 7.2.7.22a22.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(14 x + 42\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$D_7:F_7$ (as 14T24) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(35 t + 7\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + 5$ |
undefined |
| 7.2.7.22a23.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + 42 x ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(7 t + 42\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + (4 t + 6)$ |
undefined |
| 7.2.7.22a24.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(42 x + 14\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(42 t + 14\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + 2 t$ |
undefined |
| 7.2.7.22a25.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + 21 x ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$C_7^2:C_{12}$ (as 14T23) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + 21 t x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + (2 t + 3)$ |
undefined |
| 7.2.7.22a26.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(21 x + 35\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$D_7:F_7$ (as 14T24) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(21 t + 35\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + (4 t + 2)$ |
undefined |
| 7.2.7.22a27.1 |
$14$ |
$( x^{2} + 6 x + 3 )^{7} + \left(21 x + 14\right) ( x^{2} + 6 x + 3 )^{5} + 7$ |
$7$ |
$2$ |
$7$ |
$22$ |
$D_7:F_7$ (as 14T24) |
$2$ |
$6$ |
$[\frac{11}{6}]$ |
$[\frac{5}{6}]$ |
$[\frac{11}{6}, \frac{11}{6}]_{6}^{2}$ |
$[\frac{5}{6},\frac{5}{6}]_{6}^{2}$ |
$[\frac{11}{6}]_{6}$ |
$[\frac{5}{6}]_{6}$ |
$1$ |
$t^{2} + 6 t + 3$ |
$x^{7} + \left(28 t + 35\right) x^{5} + 7$ |
$[5, 0]$ |
$[1]$ |
$z + 4$ |
undefined |
