| 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 |
| 7.3.6.15a1.1 |
4 |
$( x^{3} + 6 x^{2} + 4 )^{6} + 7 x^{2}$ |
$C_{18}$ (as 18T1) |
$18$ |
$18$ |
$[\ ]_{6}^{3}$ |
$[\ ]_{6}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ |
undefined |
| 7.3.6.15a1.2 |
4 |
$( x^{3} + 6 x^{2} + 4 )^{6} + 7 x$ |
$C_{18}$ (as 18T1) |
$18$ |
$18$ |
$[\ ]_{6}^{3}$ |
$[\ ]_{6}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ |
undefined |
| 7.3.6.15a1.3 |
2 |
$( x^{3} + 6 x^{2} + 4 )^{6} + 7$ |
$C_6 \times C_3$ (as 18T2) |
$18$ |
$18$ |
$[\ ]_{6}^{3}$ |
$[\ ]_{6}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ |
$[1]$ |
| 7.3.6.15a1.4 |
2 |
$( x^{3} + 6 x^{2} + 4 )^{6} + 7 x^{2} + 21$ |
$C_6 \times C_3$ (as 18T2) |
$18$ |
$18$ |
$[\ ]_{6}^{3}$ |
$[\ ]_{6}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ |
undefined |
| 7.3.6.15a1.5 |
4 |
$( x^{3} + 6 x^{2} + 4 )^{6} + 7 x^{2} + 21 x + 21$ |
$C_{18}$ (as 18T1) |
$18$ |
$18$ |
$[\ ]_{6}^{3}$ |
$[\ ]_{6}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ |
undefined |
| 7.3.6.15a1.6 |
4 |
$( x^{3} + 6 x^{2} + 4 )^{6} + 28 x^{2} + 21 x + 21$ |
$C_{18}$ (as 18T1) |
$18$ |
$18$ |
$[\ ]_{6}^{3}$ |
$[\ ]_{6}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$[0]$ |
$[1]$ |
$z^5 + 6 z^4 + z^3 + 6 z^2 + z + 6$ |
undefined |
