| 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 |
| 2.2.8.40b8.45 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{5} + 10 x^{4} + 8 t x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.46 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 10 ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{5} + 2 x^{4} + 8 t x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.47 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{5} + 2 x^{4} + 8 t x^{3} + 8 t x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.48 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 10 ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{5} + 10 x^{4} + 8 t x^{3} + 8 t x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.75 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 2 t x^{6} + 4 x^{5} + 10 x^{4} + 8 x^{3} + 8 x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.76 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 10 ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 2 t x^{6} + 4 x^{5} + 2 x^{4} + 8 x^{3} + 8 x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.77 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 2 t x^{6} + 4 x^{5} + 2 x^{4} + \left(8 t + 8\right) x^{3} + 8 x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.78 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 10 ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 2 t x^{6} + 4 x^{5} + 10 x^{4} + \left(8 t + 8\right) x^{3} + 8 x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.121 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{5} + 10 x^{4} + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.122 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 10 ( x^{2} + x + 1 )^{4} + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{5} + 2 x^{4} + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.123 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{5} + 2 x^{4} + 8 t x^{3} + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.124 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 10 ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{5} + 10 x^{4} + 8 t x^{3} + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.153 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 2 t x^{6} + 4 x^{5} + 10 x^{4} + \left(8 t + 8\right) x + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.154 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 10 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 2 t x^{6} + 4 x^{5} + 2 x^{4} + \left(8 t + 8\right) x + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.155 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 2 t x^{6} + 4 x^{5} + 2 x^{4} + 8 t x^{3} + \left(8 t + 8\right) x + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b8.156 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 10 ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 2 t x^{6} + 4 x^{5} + 10 x^{4} + 8 t x^{3} + \left(8 t + 8\right) x + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.40b19.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + 2 t x^{4} + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + \left(2 t + 8\right) x^{4} + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + \left(2 t + 8\right) x^{4} + \left(8 t + 8\right) x^{3} + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.5 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + 2 t x^{4} + \left(8 t + 8\right) x^{3} + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.45 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + 2 t x^{4} + 8 x + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.46 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + \left(2 t + 8\right) x^{4} + 8 x + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.49 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + \left(2 t + 8\right) x^{4} + \left(8 t + 8\right) x^{3} + 8 x + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.50 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + 2 t x^{4} + \left(8 t + 8\right) x^{3} + 8 x + 2$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.86 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + \left(2 t + 8\right) x^{4} + 8 t x^{3} + 8 t x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.87 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + 2 t x^{4} + 8 t x^{3} + 8 t x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.88 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + 2 t x^{4} + 8 x^{3} + 8 t x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.89 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + \left(2 t + 8\right) x^{4} + 8 x^{3} + 8 t x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.121 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + \left(2 t + 8\right) x^{4} + 8 t x^{3} + \left(8 t + 8\right) x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.122 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + 2 t x^{4} + 8 t x^{3} + \left(8 t + 8\right) x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.125 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + 2 t x^{4} + 8 x^{3} + \left(8 t + 8\right) x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.40b19.126 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 2, \frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + \left(2 t + 2\right) x^{6} + \left(4 t + 4\right) x^{5} + \left(2 t + 8\right) x^{4} + 8 x^{3} + \left(8 t + 8\right) x + 6$ |
$[13, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + t z^2 + (t + 1),(t + 1) z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.17 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 4 t x^{6} + 2 t x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.18 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 4 t x^{6} + \left(2 t + 8\right) x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.21 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 4 t x^{6} + 2 t x^{4} + 8 t x^{3} + 4 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.22 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 4 t x^{6} + \left(2 t + 8\right) x^{4} + 8 t x^{3} + 4 x^{2} + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.29 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 4 t x^{6} + 2 t x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.30 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 4 t x^{6} + \left(2 t + 8\right) x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.33 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 4 t x^{6} + 2 t x^{4} + 4 x^{2} + 8 x + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.34 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 4 t x^{6} + \left(2 t + 8\right) x^{4} + 4 x^{2} + 8 x + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.77 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + \left(4 t + 4\right) x^{6} + 2 t x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + 8 t x + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.78 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(2 t + 8\right) x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + 8 t x + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.81 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + \left(4 t + 4\right) x^{6} + 2 t x^{4} + 8 t x^{3} + 4 x^{2} + 8 t x + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.82 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(2 t + 8\right) x^{4} + 8 t x^{3} + 4 x^{2} + 8 t x + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.91 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 8\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(2 t + 8\right) x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + \left(8 t + 8\right) x + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.92 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 8\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + \left(4 t + 4\right) x^{6} + 2 t x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + \left(8 t + 8\right) x + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.95 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 8\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(2 t + 8\right) x^{4} + 8 t x^{3} + 4 x^{2} + \left(8 t + 8\right) x + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.96 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 8\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + \left(4 t + 4\right) x^{6} + 2 t x^{4} + 8 t x^{3} + 4 x^{2} + \left(8 t + 8\right) x + 6$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.113 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 4 t x^{6} + 2 t x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.44d8.114 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_2^6.D_4$ (as 16T940) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,\frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 4 t x^{6} + \left(2 t + 8\right) x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + 1,z + (t + 1)$ |
$[1, 3, 7, 15]$ |
