| Label |
Packet size |
Polynomial |
Galois group |
Galois degree |
$\#\Aut(K/\Q_p)$ |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 7.3.7.27a1.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + 14 ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$3$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (t^2 + 6 t + 1)$ |
undefined |
| 7.3.7.27a2.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + 28 ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$F_7$ (as 21T4) |
$42$ |
$3$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (2 t^2 + 5 t + 2)$ |
undefined |
| 7.3.7.27a3.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + 42 ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$F_7$ (as 21T4) |
$42$ |
$3$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (3 t^2 + 4 t + 3)$ |
undefined |
| 7.3.7.27a4.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + 7 ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$F_7$ (as 21T4) |
$42$ |
$3$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (4 t^2 + 3 t + 4)$ |
undefined |
| 7.3.7.27a5.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + 21 ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$3$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (5 t^2 + 2 t + 5)$ |
undefined |
| 7.3.7.27a6.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + 35 ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$3$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (6 t^2 + t + 6)$ |
undefined |
| 7.3.7.27a7.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + 14 x ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (t + 3)$ |
undefined |
| 7.3.7.27a8.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x + 14\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (t^2 + 4)$ |
undefined |
| 7.3.7.27a9.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x + 28\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$C_7^3:C_6$ (as 21T31) |
$2058$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (2 t^2 + 6 t + 5)$ |
undefined |
| 7.3.7.27a10.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x + 42\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (3 t^2 + 5 t + 6)$ |
undefined |
| 7.3.7.27a11.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + 28 x ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (2 t + 6)$ |
undefined |
| 7.3.7.27a12.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(28 x + 42\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$C_7^3:C_6$ (as 21T31) |
$2058$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (3 t^2 + 6 t + 2)$ |
undefined |
| 7.3.7.27a13.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(28 x + 7\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (4 t^2 + 5 t + 3)$ |
undefined |
| 7.3.7.27a14.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(28 x + 35\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (6 t^2 + 3 t + 5)$ |
undefined |
| 7.3.7.27a15.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + 42 x ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (3 t + 2)$ |
undefined |
| 7.3.7.27a16.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(42 x + 28\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (2 t^2 + t + 4)$ |
undefined |
| 7.3.7.27a17.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(42 x + 21\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$C_7:F_7$ (as 21T19) |
$294$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (5 t^2 + 5 t)$ |
undefined |
| 7.3.7.27a18.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(42 x + 35\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$C_7^3:C_6$ (as 21T31) |
$2058$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (6 t^2 + 4 t + 1)$ |
undefined |
| 7.3.7.27a19.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + 7 x ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (4 t + 5)$ |
undefined |
| 7.3.7.27a20.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + 21 x ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (5 t + 1)$ |
undefined |
| 7.3.7.27a21.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(21 x + 42\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$C_7^3:C_6$ (as 21T31) |
$2058$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (3 t^2 + 2 t + 4)$ |
undefined |
| 7.3.7.27a22.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(21 x + 21\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (5 t^2 + 6)$ |
undefined |
| 7.3.7.27a23.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + 35 x ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (6 t + 4)$ |
undefined |
| 7.3.7.27a24.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(35 x + 7\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (4 t^2 + 2 t + 1)$ |
undefined |
| 7.3.7.27a25.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(35 x + 21\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (5 t^2 + t + 2)$ |
undefined |
| 7.3.7.27a26.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + 14 x^{2} ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (t^2 + 3 t)$ |
undefined |
| 7.3.7.27a27.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 14\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (2 t^2 + 2 t + 1)$ |
undefined |
| 7.3.7.27a28.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 28\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (3 t^2 + t + 2)$ |
undefined |
| 7.3.7.27a29.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 42\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (4 t^2 + 3)$ |
undefined |
| 7.3.7.27a30.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 35\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (4 t + 6)$ |
undefined |
| 7.3.7.27a31.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 14 x + 42\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$C_7^3:C_6$ (as 21T31) |
$2058$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (4 t^2 + t + 6)$ |
undefined |
| 7.3.7.27a32.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 28 x\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (t^2 + 5 t + 6)$ |
undefined |
| 7.3.7.27a33.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 28 x + 42\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$C_7:F_7$ (as 21T16) |
$294$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (4 t^2 + 2 t + 2)$ |
undefined |
| 7.3.7.27a34.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 42 x\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (t^2 + 6 t + 2)$ |
undefined |
| 7.3.7.27a35.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 42 x + 42\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (4 t^2 + 3 t + 5)$ |
undefined |
| 7.3.7.27a36.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 7 x + 14\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (2 t^2 + 6 t + 6)$ |
undefined |
| 7.3.7.27a37.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 7 x + 7\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$C_7^3:C_6$ (as 21T31) |
$2058$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (5 t^2 + 3 t + 2)$ |
undefined |
| 7.3.7.27a38.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 21 x + 7\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (5 t^2 + 4 t + 5)$ |
undefined |
| 7.3.7.27a39.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 21 x + 35\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + 2 t$ |
undefined |
| 7.3.7.27a40.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 35 x + 28\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (3 t^2 + 6)$ |
undefined |
| 7.3.7.27a41.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(14 x^{2} + 35 x + 42\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (4 t^2 + 6 t)$ |
undefined |
| 7.3.7.27a42.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + 28 x^{2} ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (2 t^2 + 6 t)$ |
undefined |
| 7.3.7.27a43.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(28 x^{2} + 28\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (4 t^2 + 4 t + 2)$ |
undefined |
| 7.3.7.27a44.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(28 x^{2} + 7\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (6 t^2 + 2 t + 4)$ |
undefined |
| 7.3.7.27a45.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(28 x^{2} + 35\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
$C_7^3:C_6$ (as 21T31) |
$2058$ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (t^2 + 6)$ |
undefined |
| 7.3.7.27a46.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(28 x^{2} + 28 x + 14\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + 3 t^2$ |
undefined |
| 7.3.7.27a47.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(28 x^{2} + 28 x + 28\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (4 t^2 + 6 t + 1)$ |
undefined |
| 7.3.7.27a48.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(28 x^{2} + 28 x + 7\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (6 t^2 + 4 t + 3)$ |
undefined |
| 7.3.7.27a49.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(28 x^{2} + 28 x + 35\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[1]$ |
$z^3 + (t^2 + 2 t + 5)$ |
undefined |
| 7.3.7.27a50.1 |
|
$( x^{3} + 6 x^{2} + 4 )^{7} + \left(28 x^{2} + 42 x\right) ( x^{3} + 6 x^{2} + 4 )^{3} + 7$ |
not computed |
$ $not computed$ $ |
$1$ |
not computed |
not computed |
not computed |
not computed |
$[3, 0]$ |
$[3]$ |
$z^3 + (2 t^2 + 2 t + 2)$ |
undefined |
