| 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 |
| 2.2.8.56a3.609 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 4 t x^{4} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.610 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 16\right) x^{4} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.611 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 16\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.612 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.737 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 4 t x^{4} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.738 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 16\right) x^{4} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.739 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(4 t + 16\right) x^{4} + 16 t x^{3} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.740 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + \left(16 t + 16\right) x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1641 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1642 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 28\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1643 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1644 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 28\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 24\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1701 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1702 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 16\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1703 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 4 t x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.1704 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 20\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(4 t + 16\right) x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.514 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.518 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.554 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.558 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.564 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.568 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.604 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 16 x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.608 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.668 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.672 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(20 t + 8\right) x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.713 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 16 x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.717 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 4 t x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.748 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.752 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 20 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.761 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.765 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1579 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1583 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1625 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 16 x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1629 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1642 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1646 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1660 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1664 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(20 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1683 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1687 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 16 x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1730 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1734 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 12\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 16 t x^{3} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1772 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1776 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 20 t x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1785 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a5.1789 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2.C_2^2$ (as 16T661) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{15}{4}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{11}{4},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{15}{4}]$ |
$[1,1,\frac{5}{2},\frac{11}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(4 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 3, 7, 15]$ |
