| 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 |
| 2.9.2.18a2.1 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + 2 x ( x^{9} + x^{4} + 1 ) + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{4} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.9.2.18a3.1 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + 2 x^{3} ( x^{9} + x^{4} + 1 ) + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{8} + 2 t^{5} + 2 t^{4} + 2 t^{2} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^2)$ |
$[1, 3]$ |
| 2.9.2.18a5.1 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{4} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{8} + 2 t^{5} + 2 t^{2}\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^8 + t^7 + t^4 + t^3 + 1)$ |
$[1, 3]$ |
| 2.9.2.18a8.1 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{5} + 2 x^{3} + 2\right) ( x^{9} + x^{4} + 1 ) + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^4 + t^2)$ |
$[1, 3]$ |
| 2.9.2.18a9.1 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{2}\right) ( x^{9} + x^{4} + 1 ) + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{7} + 2 t^{4} + 2 t^{3}\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + t + 1)$ |
$[1, 3]$ |
| 2.9.2.18a10.1 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{3} + 2\right) ( x^{9} + x^{4} + 1 ) + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{8} + 2 t^{7} + 2 t^{5} + 2 t^{2} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^8 + t^6 + t^5 + t^4 + t^2 + 1)$ |
$[1, 3]$ |
| 2.9.2.18a14.2 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{4} + 2 x^{3} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 4 x + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{8} + 2 t^{7} + 2 t^{6} + 2 t^{5} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^8 + t^7 + t^6 + t^5 + t^3 + t^2)$ |
$[1, 3]$ |
| 2.9.2.18a15.2 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{6} + 2 x^{5} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 4 x + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{8} + 2 t^{7} + 2 t^{6} + 2 t^{3} + 2 t^{2} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^8 + t^5 + t^4)$ |
$[1, 3]$ |
| 2.9.2.18a22.2 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{5} + 2 x^{4} + 2 x^{2}\right) ( x^{9} + x^{4} + 1 ) + 4 x^{2} + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{4} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^8 + t^7 + t^6 + t^4 + t^3)$ |
$[1, 3]$ |
| 2.9.2.18a23.2 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{6} + 2 x^{2} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 4 x + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{7} + 2 t^{5} + 2 t^{3} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^5)$ |
$[1, 3]$ |
| 2.9.2.18a25.2 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{6} + 2 x^{4} + 2 x^{3} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 4 x^{2} + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{8} + 2 t^{7} + 2 t^{6} + 2 t^{5} + 2 t^{4} + 2 t^{3} + 2 t^{2} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^7 + t^3 + t^2 + t)$ |
$[1, 3]$ |
| 2.9.2.18a27.2 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{7} + 2 x^{6} + 2 x^{5} + 2 x^{4} + 2 x + 2\right) ( x^{9} + x^{4} + 1 ) + 4 x + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{8} + 2 t^{7} + 2 t^{4} + 2 t^{3} + 2 t^{2} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^7 + t^6 + t^4 + t^3 + t)$ |
$[1, 3]$ |
| 2.9.2.18a29.1 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{8} + 2 x^{4} + 2 x^{2} + 2\right) ( x^{9} + x^{4} + 1 ) + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{8} + 2 t^{6} + 2 t^{5} + 2 t^{4} + 2 t^{2} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^8 + t^6 + t^5 + t^3 + t^2 + t)$ |
$[1, 3]$ |
| 2.9.2.18a32.2 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{8} + 2 x^{5} + 2 x^{4}\right) ( x^{9} + x^{4} + 1 ) + 4 x^{3} + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{8} + 2 t^{3} + 2 t^{2} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^8 + t^6 + t^4 + t^3 + t^2)$ |
$[1, 3]$ |
| 2.9.2.18a33.1 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{8} + 2 x^{5} + 2 x^{4} + 2 x^{3} + 2\right) ( x^{9} + x^{4} + 1 ) + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{8} + 2 t^{7} + 2 t^{6} + 2 t^{4} + 2 t^{3} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + t^3)$ |
$[1, 3]$ |
| 2.9.2.18a34.2 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{8} + 2 x^{5} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 4 x^{2} + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{8} + 2 t^{4} + 2 t^{2} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^8 + t^5 + t^3 + t + 1)$ |
$[1, 3]$ |
| 2.9.2.18a39.1 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{8} + 2 x^{6} + 2 x^{4} + 2 x^{3} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{2} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^3)$ |
$[1, 3]$ |
| 2.9.2.18a42.2 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{8} + 2 x^{6} + 2 x^{5} + 2 x^{3} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 4 x + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{8} + 2 t^{6} + 2 t^{2} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^8 + t^7 + t^5 + t^4)$ |
$[1, 3]$ |
| 2.9.2.18a45.2 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{8} + 2 x^{6} + 2 x^{5} + 2 x^{4} + 2 x^{3} + 2\right) ( x^{9} + x^{4} + 1 ) + 4 x + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{8} + 2 t^{7} + 2 t^{6} + 2 t^{4} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^3 + 1)$ |
$[1, 3]$ |
| 2.9.2.18a51.1 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{8} + 2 x^{7} + 2 x^{5} + 2 x^{3} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{6} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^8 + t^7 + t^6 + t^5 + t + 1)$ |
$[1, 3]$ |
| 2.9.2.18a55.1 |
$18$ |
$( x^{9} + x^{4} + 1 )^{2} + \left(2 x^{8} + 2 x^{7} + 2 x^{6} + 2 x^{2} + 2 x\right) ( x^{9} + x^{4} + 1 ) + 2$ |
$2$ |
$9$ |
$2$ |
$18$ |
$C_2^8:C_9$ (as 18T368) |
$9$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2, 2]^{9}$ |
$[1,1,1,1,1,1,1,1]^{9}$ |
$[2,2,2,2,2,2,2]$ |
$[1,1,1,1,1,1,1]$ |
$2$ |
$t^{9} + t^{4} + 1$ |
$x^{2} + \left(2 t^{3} + 2 t^{2} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^7 + t^5 + t^2)$ |
$[1, 3]$ |
