| 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 |
| 2.2.8.54a2.161 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T947) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.162 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T947) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 2 t x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.163 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T957) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.164 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T957) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.165 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T957) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.166 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T957) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.167 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T947) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 2 t x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.168 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T947) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.345 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T957) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.346 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T957) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.347 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T947) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.348 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T947) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.349 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T947) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.350 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T947) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.351 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T957) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.352 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T957) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.417 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.418 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.419 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.420 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.421 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.422 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.423 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.424 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.489 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.490 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.491 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.492 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.493 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.494 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 2 t x^{4} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.495 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 2 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.496 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.673 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.674 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 2 t x^{4} + 16 t x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.675 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 2 t x^{4} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.676 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.677 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 16 t x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.678 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.679 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.680 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.681 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.682 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 2 t x^{4} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.683 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 2 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.684 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.685 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.686 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.687 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.688 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.857 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 18\right) x^{4} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.858 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T1011) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
