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 |
3.2.6.22a1.4 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + 9 x ( x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$6$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{5}{2}]_{2}^{6}$ |
$[\frac{1}{2},\frac{3}{2}]_{2}^{6}$ |
$[\frac{3}{2}]^{3}$ |
$[\frac{1}{2}]^{3}$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x^{3} + 9 t x^{2} + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.8 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$6$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{5}{2}]_{2}^{6}$ |
$[\frac{1}{2},\frac{3}{2}]_{2}^{6}$ |
$[\frac{3}{2}]^{3}$ |
$[\frac{1}{2}]^{3}$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x^{3} + \left(18 t + 18\right) x^{2} + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.12 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$6$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{5}{2}]_{2}^{6}$ |
$[\frac{1}{2},\frac{3}{2}]_{2}^{6}$ |
$[\frac{3}{2}]^{3}$ |
$[\frac{1}{2}]^{3}$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x^{3} + \left(9 t + 18\right) x^{2} + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.19 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 18 x ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]_{2}^{2}$ |
$[1,1,\frac{3}{2}]_{2}^{2}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x^{2} + \left(9 t + 18\right) x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.20 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + 18 x ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]_{2}^{2}$ |
$[1,1,\frac{3}{2}]_{2}^{2}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x^{3} + 9 x^{2} + 9 t x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.21 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + 18 x ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]_{2}^{2}$ |
$[1,1,\frac{3}{2}]_{2}^{2}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{3} + 9 x^{2} + 9 t x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.28 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]_{2}^{2}$ |
$[1,1,\frac{3}{2}]_{2}^{2}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{2} + \left(9 t + 18\right) x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.29 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]_{2}^{2}$ |
$[1,1,\frac{3}{2}]_{2}^{2}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{3} + 18 x^{2} + \left(9 t + 18\right) x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.30 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]_{2}^{2}$ |
$[1,1,\frac{3}{2}]_{2}^{2}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x^{3} + 18 x^{2} + \left(9 t + 18\right) x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.37 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]_{2}^{2}$ |
$[1,1,\frac{3}{2}]_{2}^{2}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(9 t + 18\right) x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.38 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]_{2}^{2}$ |
$[1,1,\frac{3}{2}]_{2}^{2}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{3} + \left(9 t + 18\right) x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.39 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + 9 x ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, 2, \frac{5}{2}]_{2}^{2}$ |
$[1,1,\frac{3}{2}]_{2}^{2}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x^{3} + \left(9 t + 18\right) x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.43 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 x ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2},2]$ |
$[\frac{1}{2},1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 t x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.44 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + 9 x ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2},2]$ |
$[\frac{1}{2},1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x^{3} + \left(18 t + 9\right) x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.45 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + 9 x ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2},2]$ |
$[\frac{1}{2},1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{3} + 9 t x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.49 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2},2]$ |
$[\frac{1}{2},1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(18 t + 18\right) x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.50 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2},2]$ |
$[\frac{1}{2},1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x^{3} + \left(18 t + 18\right) x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.51 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2},2]$ |
$[\frac{1}{2},1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{3} + \left(18 t + 18\right) x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.55 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2},2]$ |
$[\frac{1}{2},1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + \left(9 t + 18\right) x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.56 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2},2]$ |
$[\frac{1}{2},1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 9 x^{3} + 18 t x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.57 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 18 ( x^{2} + 2 x + 2 )^{3} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, 2, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},1,\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2},2]$ |
$[\frac{1}{2},1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{3} + \left(9 t + 18\right) x^{2} + 9 x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.62 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + 18 x ( x^{2} + 2 x + 2 )^{2} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$6$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{6}$ |
$[1,\frac{3}{2}]_{2}^{6}$ |
$[2]^{3}$ |
$[1]^{3}$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{3} + 9 x^{2} + \left(9 t + 9\right) x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.67 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + \left(18 x + 9\right) ( x^{2} + 2 x + 2 )^{2} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$6$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{6}$ |
$[1,\frac{3}{2}]_{2}^{6}$ |
$[2]^{3}$ |
$[1]^{3}$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{3} + 18 x^{2} + \left(9 t + 9\right) x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |
3.2.6.22a1.72 |
$12$ |
$( x^{2} + 2 x + 2 )^{6} + 9 ( x^{2} + 2 x + 2 )^{3} + \left(18 x + 18\right) ( x^{2} + 2 x + 2 )^{2} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$6$ |
$22$ |
$C_3\times S_3^2$ (as 12T70) |
$6$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[2, \frac{5}{2}]_{2}^{6}$ |
$[1,\frac{3}{2}]_{2}^{6}$ |
$[2]^{3}$ |
$[1]^{3}$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{6} + 18 x^{3} + \left(9 t + 9\right) x + 3$ |
$[6, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 2$ |
$[1, 7]$ |