| 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 |
| 2.6.2.12a1.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 2 ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{6}$ |
$[1]^{6}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 1)$ |
$[1, 2]$ |
| 2.6.2.12a1.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 2 ( x^{6} + x^{4} + x^{3} + x + 1 ) + 4 x^{3} + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_{12}$ (as 12T1) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{6}$ |
$[1]^{6}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 2 x + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 1)$ |
$[1, 4]$ |
| 2.6.2.12a2.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 2 x ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$D_4\times A_4$ (as 12T51) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{6}$ |
$[1,1,1,1]^{6}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 2 t^{2} x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + t)$ |
$[1, 3]$ |
| 2.6.2.12a2.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 2 x ( x^{6} + x^{4} + x^{3} + x + 1 ) + 6$ |
$2$ |
$6$ |
$2$ |
$12$ |
$D_4\times A_4$ (as 12T51) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{6}$ |
$[1,1,1,1]^{6}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 2 t^{4} x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + t)$ |
$[1, 3]$ |
| 2.6.2.12a3.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 2 x^{3} ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2^3:A_4$ (as 12T58) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{6}$ |
$[1,1,1,1]^{6}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t^{2} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^3)$ |
$[1, 3]$ |
| 2.6.2.12a3.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 2 x^{3} ( x^{6} + x^{4} + x^{3} + x + 1 ) + 4 x + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2^4:C_{12}$ (as 12T105) |
$12$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{12}$ |
$[1,1,1,1]^{12}$ |
$[2,2,2]^{2}$ |
$[1,1,1]^{2}$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2 t^{2} + 2 t + 2\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^3)$ |
$[1, 3]$ |
| 2.6.2.12a4.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{3} + 2\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$[1,1,1,1,1,1]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3}\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^3 + t^2 + 1)$ |
$[1, 3]$ |
| 2.6.2.12a4.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{3} + 2\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 6$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$[1,1,1,1,1,1]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3}\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^3 + t^2 + 1)$ |
$[1, 3]$ |
| 2.6.2.12a5.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{3} + 2 x^{2} + 2 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{6}$ |
$[1,1]^{6}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t^{2} + 2 t\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^4 + t^2 + t)$ |
$[1, 3]$ |
| 2.6.2.12a5.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{3} + 2 x^{2} + 2 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 6$ |
$2$ |
$6$ |
$2$ |
$12$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{6}$ |
$[1,1]^{6}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t^{2} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^4 + t^2 + t)$ |
$[1, 3]$ |
| 2.6.2.12a6.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{4} + 2 x^{3} + 2\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2]^{6}$ |
$[1,1,1,1,1]^{6}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3}\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^2 + t)$ |
$[1, 3]$ |
| 2.6.2.12a6.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{4} + 2 x^{3} + 2\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2^4:C_{12}$ (as 12T105) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2]^{6}$ |
$[1,1,1,1,1]^{6}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3}\right) x + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^2 + t)$ |
$[1, 3]$ |
| 2.6.2.12a7.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 2 x^{5} ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$[1,1,1,1,1,1]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + t^2 + t)$ |
$[1, 3]$ |
| 2.6.2.12a7.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 2 x^{5} ( x^{6} + x^{4} + x^{3} + x + 1 ) + 6$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$[1,1,1,1,1,1]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + t^2 + t)$ |
$[1, 3]$ |
| 2.6.2.12a8.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{2}\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$[1,1,1,1,1,1]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{2}\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t$ |
$[1, 3]$ |
| 2.6.2.12a8.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{2}\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 6$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$[1,1,1,1,1,1]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{2}\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + t$ |
$[1, 3]$ |
| 2.6.2.12a9.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{2}\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$A_4 \times C_2$ (as 12T7) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{6}$ |
$[1,1]^{6}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + 1)$ |
$[1, 3]$ |
| 2.6.2.12a9.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{2}\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_4\times A_4$ (as 12T29) |
$12$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{12}$ |
$[1,1]^{12}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$4$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2 t\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + 1)$ |
$[1, 3]$ |
| 2.6.2.12a10.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{2} + 2\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2^2 \times A_4$ (as 12T25) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{6}$ |
$[1,1,1]^{6}$ |
$[2,2]$ |
$[1,1]$ |
$4$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + t^2)$ |
$[1, 3]$ |
| 2.6.2.12a10.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{2} + 2\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 4 x + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_4\times A_4$ (as 12T29) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{6}$ |
$[1,1,1]^{6}$ |
$[2,2]$ |
$[1,1]$ |
$4$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + t^2)$ |
$[1, 3]$ |
| 2.6.2.12a11.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{2} + 2 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2^3:A_4$ (as 12T58) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{6}$ |
$[1,1,1,1]^{6}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{2} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t + 1)$ |
$[1, 3]$ |
| 2.6.2.12a11.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{2} + 2 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 4 x + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2^4:C_{12}$ (as 12T105) |
$12$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{12}$ |
$[1,1,1,1]^{12}$ |
$[2,2,2]^{2}$ |
$[1,1,1]^{2}$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t + 2\right) x + 4 t^{4} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t + 1)$ |
$[1, 3]$ |
| 2.6.2.12a12.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{3}\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2^4:C_{12}$ (as 12T105) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2]^{6}$ |
$[1,1,1,1,1]^{6}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t^{2} + 2 t\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^4 + t^2 + 1)$ |
$[1, 3]$ |
| 2.6.2.12a12.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{3}\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2]^{6}$ |
$[1,1,1,1,1]^{6}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^4 + t^2 + 1)$ |
$[1, 3]$ |
| 2.6.2.12a13.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{3} + 2\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$[1,1,1,1,1,1]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^4)$ |
$[1, 3]$ |
| 2.6.2.12a13.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{3} + 2\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 6$ |
$2$ |
$6$ |
$2$ |
$12$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{6}$ |
$[1,1,1,1,1,1]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t^{2} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^4)$ |
$[1, 3]$ |
| 2.6.2.18a1.1 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{6}$ |
$[2]^{6}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.2 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_{12}$ (as 12T1) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{6}$ |
$[2]^{6}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.3 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 4 x^{3} ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$[1,1,1,1,1,2]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.4 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 4 x^{3} ( x^{6} + x^{4} + x^{3} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$[1,1,1,1,1,2]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.5 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{4} + 4 x^{3}\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$D_4\times A_4$ (as 12T51) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 3]^{6}$ |
$[1,1,1,2]^{6}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{3} + 4 t^{2}\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.6 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{4} + 4 x^{3}\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$D_4\times A_4$ (as 12T51) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 3]^{6}$ |
$[1,1,1,2]^{6}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t + 4\right) x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.7 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 4 x ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$[1,1,1,1,2]^{6}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.8 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 4 x ( x^{6} + x^{4} + x^{3} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2^4:C_{12}$ (as 12T105) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$[1,1,1,1,2]^{6}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 4 t x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.9 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{3} + 4 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$[1,1,1,1,1,2]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.10 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{3} + 4 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$[1,1,1,1,1,2]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4\right) x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.11 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{2} + 4 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$[1,1,1,1,2]^{6}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{2} + 4 t + 4\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.12 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{2} + 4 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2^4:C_{12}$ (as 12T105) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$[1,1,1,1,2]^{6}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4}\right) x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.13 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{4} + 4 x^{2} + 4 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2^2 \times A_4$ (as 12T25) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 3]^{6}$ |
$[1,1,2]^{6}$ |
$[2,2]$ |
$[1,1]$ |
$4$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{2}\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.14 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{4} + 4 x^{2} + 4 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_4\times A_4$ (as 12T29) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 3]^{6}$ |
$[1,1,2]^{6}$ |
$[2,2]$ |
$[1,1]$ |
$4$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{2}\right) x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.15 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 3]^{6}$ |
$[1,2]^{6}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.16 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$D_4 \times C_3$ (as 12T14) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 3]^{6}$ |
$[1,2]^{6}$ |
$[2]$ |
$[1]$ |
$6$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.17 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 4 ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{6}$ |
$[2]^{6}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 4 x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.18 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + 4 ( x^{6} + x^{4} + x^{3} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_{12}$ (as 12T1) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{6}$ |
$[2]^{6}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + 4 x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.19 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{3} + 4\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$[1,1,1,1,1,2]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t^{2} + 4 t\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.20 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{3} + 4\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$[1,1,1,1,1,2]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{3} + 4 t^{2} + 4 t\right) x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.21 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x + 4\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2^4:A_4$ (as 12T87) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$[1,1,1,1,2]^{6}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{4} + 4 t\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.22 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x + 4\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2^4:C_{12}$ (as 12T105) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{6}$ |
$[1,1,1,1,2]^{6}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{2} + 4\right) x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.23 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{3} + 4 x + 4\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$[1,1,1,1,1,2]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2}\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.6.2.18a1.24 |
$12$ |
$( x^{6} + x^{4} + x^{3} + x + 1 )^{2} + \left(4 x^{3} + 4 x + 4\right) ( x^{6} + x^{4} + x^{3} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$6$ |
$2$ |
$18$ |
$C_2\wr C_6$ (as 12T134) |
$6$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 3]^{6}$ |
$[1,1,1,1,1,2]^{6}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{6} + t^{4} + t^{3} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2}\right) x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
