| 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 |
| 2.16.1.0a1.1 |
$16$ |
$x^{16} + x^{5} + x^{3} + x^{2} + 1$ |
$2$ |
$16$ |
$1$ |
$0$ |
$C_{16}$ (as 16T1) |
$16$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{16}$ |
$[\ ]^{16}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{16} + t^{5} + t^{3} + t^{2} + 1$ |
$x - 2$ |
$[\ ]$ |
$[\ ]$ |
|
$[1]$ |
| 2.8.2.16a1.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + 2 ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_8\times C_2$ (as 16T5) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{8}$ |
$[1]^{8}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 2]$ |
| 2.8.2.16a1.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + 2 ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 4 x^{5} + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_{16}$ (as 16T1) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{8}$ |
$[1]^{8}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + 2 x + 4 t^{5} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 4]$ |
| 2.8.2.16a2.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + 2 x ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^7:C_8$ (as 16T1194) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + 2 t x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t$ |
$[1, 3]$ |
| 2.8.2.16a2.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + 2 x ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 4 x^{7} + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^7.C_8$ (as 16T1223) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + 2 t x + 4 t^{7} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t$ |
$[1, 3]$ |
| 2.8.2.16a3.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t + 1)$ |
$[1, 3]$ |
| 2.8.2.16a3.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 6$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t + 1)$ |
$[1, 3]$ |
| 2.8.2.16a4.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + 2 x^{3} ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + 2 t^{3} x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + t^3$ |
$[1, 3]$ |
| 2.8.2.16a4.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + 2 x^{3} ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 6$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + 2 t^{3} x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t^3$ |
$[1, 3]$ |
| 2.8.2.16a5.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{3} + 2 x\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^4.C_8$ (as 16T306) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{8}$ |
$[1,1,1,1]^{8}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$4$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{3} + 2 t\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + t)$ |
$[1, 3]$ |
| 2.8.2.16a5.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{3} + 2 x\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 4 x + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^4:C_8$ (as 16T258) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{8}$ |
$[1,1,1,1]^{8}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$4$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{3} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + t)$ |
$[1, 3]$ |
| 2.8.2.16a6.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{3} + 2 x^{2}\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{2} + 2 t + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + t^2)$ |
$[1, 3]$ |
| 2.8.2.16a6.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{3} + 2 x^{2}\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 6$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{2} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + t^2)$ |
$[1, 3]$ |
| 2.8.2.16a7.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + 2 x^{5} ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + 2 t^{5} x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t^5$ |
$[1, 3]$ |
| 2.8.2.16a7.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + 2 x^{5} ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 6$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + 2 t^{5} x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + t^5$ |
$[1, 3]$ |
| 2.8.2.16a8.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{5} + 2 x + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^6:C_8$ (as 16T817) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t + 1)$ |
$[1, 3]$ |
| 2.8.2.16a8.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{5} + 2 x + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 4 x + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^6.C_8$ (as 16T841) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t + 2\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t + 1)$ |
$[1, 3]$ |
| 2.8.2.16a9.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{5} + 2 x^{2} + 2 x\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{2}\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^2 + t)$ |
$[1, 3]$ |
| 2.8.2.16a9.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{5} + 2 x^{2} + 2 x\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 6$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{2}\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^2 + t)$ |
$[1, 3]$ |
| 2.8.2.16a10.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{5} + 2 x^{3}\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3}\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^3)$ |
$[1, 3]$ |
| 2.8.2.16a10.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{5} + 2 x^{3}\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 6$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3}\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^3)$ |
$[1, 3]$ |
| 2.8.2.16a11.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{5} + 2 x^{4}\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^6:C_8$ (as 16T817) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^4)$ |
$[1, 3]$ |
| 2.8.2.16a11.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{5} + 2 x^{4}\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 4 x^{4} + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^6.C_8$ (as 16T841) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t\right) x + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^4)$ |
$[1, 3]$ |
| 2.8.2.16a12.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{2} + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^6:C_8$ (as 16T817) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^4 + t^2 + 1)$ |
$[1, 3]$ |
| 2.8.2.16a12.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{2} + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 4 x + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^6.C_8$ (as 16T841) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2\right) x + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^4 + t^2 + 1)$ |
$[1, 3]$ |
| 2.8.2.16a13.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{3} + 2 x\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^5.C_8$ (as 16T591) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1]^{8}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{2} + 2\right) x + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^4 + t^3 + t)$ |
$[1, 3]$ |
| 2.8.2.16a13.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{3} + 2 x\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 4 x^{3} + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^5:C_8$ (as 16T565) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1]^{8}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{2} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + t^4 + t^3 + t)$ |
$[1, 3]$ |
| 2.8.2.16a14.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{6} + 2 x^{3} + 2 x\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{3} + 2 t\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^3 + t)$ |
$[1, 3]$ |
| 2.8.2.16a14.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{6} + 2 x^{3} + 2 x\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 6$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{3} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^3 + t)$ |
$[1, 3]$ |
| 2.8.2.16a15.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{6} + 2 x^{4} + 2 x^{3} + 2 x\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^7.C_8$ (as 16T1223) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t^{2} + 2 t\right) x + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^4 + t^3 + t)$ |
$[1, 3]$ |
| 2.8.2.16a15.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{6} + 2 x^{4} + 2 x^{3} + 2 x\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 4 x + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^7:C_8$ (as 16T1194) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t^{2} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^4 + t^3 + t)$ |
$[1, 3]$ |
| 2.8.2.16a16.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{6} + 2 x^{5} + 2 x^{3} + 2 x^{2} + 2 x + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{3} + 2 t^{2} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + t^3 + t^2 + t + 1)$ |
$[1, 3]$ |
| 2.8.2.16a16.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{6} + 2 x^{5} + 2 x^{3} + 2 x^{2} + 2 x + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 6$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{3} + 2 t^{2} + 2 t + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + t^3 + t^2 + t + 1)$ |
$[1, 3]$ |
| 2.8.2.16a17.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{6} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + t^4 + t^2 + 1)$ |
$[1, 3]$ |
| 2.8.2.16a17.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{6} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 6$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + t^4 + t^2 + 1)$ |
$[1, 3]$ |
| 2.8.2.16a18.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{6} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2 x + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + t^4 + t^2 + t + 1)$ |
$[1, 3]$ |
| 2.8.2.16a18.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{6} + 2 x^{5} + 2 x^{4} + 2 x^{2} + 2 x + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 6$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + t^4 + t^2 + t + 1)$ |
$[1, 3]$ |
| 2.8.2.16a19.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{6} + 2 x^{5} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{3} + 2 t^{2} + 2 t\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)$ |
$[1, 3]$ |
| 2.8.2.16a19.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{6} + 2 x^{5} + 2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 6$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{3} + 2 t^{2} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + t^4 + t^3 + t^2 + t + 1)$ |
$[1, 3]$ |
| 2.8.2.16a20.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + 2 x^{7} ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^7.C_8$ (as 16T1223) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t^7$ |
$[1, 3]$ |
| 2.8.2.16a20.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + 2 x^{7} ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 4 x + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^7:C_8$ (as 16T1194) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t^7$ |
$[1, 3]$ |
| 2.8.2.16a21.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{7} + 2 x^{2} + 2 x + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{2} + 2 t\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^7 + t^2 + t + 1)$ |
$[1, 3]$ |
| 2.8.2.16a21.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{7} + 2 x^{2} + 2 x + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 6$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2\wr C_8$ (as 16T1351) |
not computed |
$1$ |
$[2]$ |
$[1]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{2} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^7 + t^2 + t + 1)$ |
$[1, 3]$ |
| 2.8.2.16a22.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{7} + 2 x^{4} + 2 x + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^3:C_8$ (as 16T85) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{8}$ |
$[1,1,1]^{8}$ |
$[2,2]$ |
$[1,1]$ |
$4$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{3} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^7 + t^4 + t + 1)$ |
$[1, 3]$ |
| 2.8.2.16a22.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{7} + 2 x^{4} + 2 x + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 4 x + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$\OD_{32}:C_2$ (as 16T104) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{8}$ |
$[1,1,1]^{8}$ |
$[2,2]$ |
$[1,1]$ |
$4$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{3} + 2 t + 2\right) x + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^7 + t^4 + t + 1)$ |
$[1, 3]$ |
| 2.8.2.16a23.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{7} + 2 x^{4} + 2 x^{3}\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^4.C_8$ (as 16T306) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{8}$ |
$[1,1,1,1]^{8}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$4$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{3} + 2 t^{2} + 2 t\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^7 + t^4 + t^3)$ |
$[1, 3]$ |
| 2.8.2.16a23.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{7} + 2 x^{4} + 2 x^{3}\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 4 x^{4} + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^4:C_8$ (as 16T258) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{8}$ |
$[1,1,1,1]^{8}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$4$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{3} + 2 t^{2} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^7 + t^4 + t^3)$ |
$[1, 3]$ |
| 2.8.2.16a24.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{7} + 2 x^{5}\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^7:C_8$ (as 16T1194) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{2} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^7 + t^5)$ |
$[1, 3]$ |
| 2.8.2.16a24.2 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{7} + 2 x^{5}\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 4 x^{2} + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^7.C_8$ (as 16T1223) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{2} + 2 t + 2\right) x + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^7 + t^5)$ |
$[1, 3]$ |
| 2.8.2.16a25.1 |
$16$ |
$( x^{8} + x^{4} + x^{3} + x^{2} + 1 )^{2} + \left(2 x^{7} + 2 x^{5} + 2\right) ( x^{8} + x^{4} + x^{3} + x^{2} + 1 ) + 2$ |
$2$ |
$8$ |
$2$ |
$16$ |
$C_2^7.C_8$ (as 16T1223) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{8}$ |
$[1,1,1,1,1,1,1]^{8}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{8} + t^{4} + t^{3} + t^{2} + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{2} + 2 t\right) x + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^7 + t^5 + 1)$ |
$[1, 3]$ |
