| 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 |
| 3.2.9.36b1.32 |
$18$ |
$( x^{2} + 2 x + 2 )^{9} + 9 x ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$9$ |
$36$ |
$S_3\times D_9$ (as 18T50) |
not computed |
not computed |
$[\frac{3}{2}, \frac{5}{2}]$ |
$[\frac{1}{2},\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 2 t + 2$ |
$x^{9} + \left(18 t + 9\right) x^{4} + 6 x^{3} + 18 x^{2} + 9 x + 3$ |
$[10, 3, 0]$ |
$[1, 1]$ |
$z^3 + (t + 1),(t + 1) z + 2$ |
undefined |
| 3.2.9.36b4.40 |
$18$ |
$( x^{2} + 2 x + 2 )^{9} + 9 ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$9$ |
$36$ |
$S_3\times D_9$ (as 18T50) |
not computed |
not computed |
$[\frac{3}{2}, \frac{5}{2}]$ |
$[\frac{1}{2},\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 2 t + 2$ |
$x^{9} + 18 x^{4} + 6 x^{3} + \left(9 t + 9\right) x^{2} + \left(18 t + 18\right) x + 3$ |
$[10, 3, 0]$ |
$[1, 1]$ |
$z^3 + (t + 1),(t + 1) z + (2 t + 2)$ |
undefined |
| 3.2.9.36b4.42 |
$18$ |
$( x^{2} + 2 x + 2 )^{9} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{4} + 6 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$9$ |
$36$ |
$S_3\times D_9$ (as 18T50) |
not computed |
not computed |
$[\frac{3}{2}, \frac{5}{2}]$ |
$[\frac{1}{2},\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 2 t + 2$ |
$x^{9} + \left(9 t + 9\right) x^{4} + 6 x^{3} + \left(9 t + 9\right) x^{2} + \left(18 t + 18\right) x + 3$ |
$[10, 3, 0]$ |
$[1, 1]$ |
$z^3 + (t + 1),(t + 1) z + (2 t + 2)$ |
undefined |
| 3.2.9.52a1.34 |
$18$ |
$( x^{2} + 2 x + 2 )^{9} + \left(27 x + 27\right) ( x^{2} + 2 x + 2 )^{4} + 54 ( x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$2$ |
$9$ |
$52$ |
$S_3\times D_9$ (as 18T50) |
not computed |
not computed |
$[\frac{5}{2}, \frac{7}{2}]$ |
$[\frac{3}{2},\frac{5}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t^{2} + 2 t + 2$ |
$x^{9} + \left(54 t + 54\right) x^{4} + 54 x^{2} + 3$ |
$[18, 9, 0]$ |
$[1, 1]$ |
$z^3 + (t + 1),(t + 1) z + 2$ |
undefined |
| 3.1.18.37c4.42 |
$18$ |
$x^{18} + 18 x^{8} + 9 x^{7} + 6 x^{6} + 9 x^{5} + 18 x^{4} + 9 x^{2} + 3$ |
$3$ |
$1$ |
$18$ |
$37$ |
$S_3\times D_9$ (as 18T50) |
not computed |
not computed |
$[\frac{3}{2}, \frac{5}{2}]$ |
$[\frac{1}{2},\frac{3}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 1$ |
$x^{18} + 18 x^{8} + 9 x^{7} + 6 x^{6} + 9 x^{5} + 18 x^{4} + 9 x^{2} + 3$ |
$[20, 6, 0]$ |
$[1, 2, 2]$ |
$z^9 + 2,2 z^6 + 2,2 z^2 + 2$ |
$[1, 5, 23]$ |
| 3.1.18.45a4.389 |
$18$ |
$x^{18} + 9 x^{17} + 9 x^{13} + 6 x^{12} + 18 x^{10} + 6$ |
$3$ |
$1$ |
$18$ |
$45$ |
$S_3\times D_9$ (as 18T50) |
not computed |
not computed |
$[2, 3]$ |
$[1,2]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 1$ |
$x^{18} + 9 x^{17} + 9 x^{13} + 6 x^{12} + 18 x^{10} + 6$ |
$[28, 12, 0]$ |
$[1, 2, 2]$ |
$z^9 + 2,2 z^6 + 2,2 z^2 + 2$ |
undefined |
| 3.1.18.53a2.443 |
$18$ |
$x^{18} + 27 x^{8} + 27 x^{7} + 9 x^{6} + 27 x^{4} + 27 x^{2} + 6$ |
$3$ |
$1$ |
$18$ |
$53$ |
$S_3\times D_9$ (as 18T50) |
not computed |
not computed |
$[\frac{5}{2}, \frac{7}{2}]$ |
$[\frac{3}{2},\frac{5}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$1$ |
$t + 1$ |
$x^{18} + 27 x^{8} + 27 x^{7} + 9 x^{6} + 27 x^{4} + 27 x^{2} + 6$ |
$[36, 18, 0]$ |
$[1, 2, 2]$ |
$z^9 + 2,2 z^6 + 2,2 z^2 + 2$ |
undefined |
