| 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 |
| 2.2.8.56a3.73 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T690) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 16 x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.74 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T690) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.75 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T690) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.76 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T690) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 16 x^{4} + 8 t x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.85 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + 16 t x^{3} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.86 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + 16 x^{4} + 16 t x^{3} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.87 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + 16 x^{4} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.88 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.89 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T694) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 24 x^{4} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.90 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T694) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 8 x^{4} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.91 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T694) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 8 x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.92 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T694) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 24 x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.105 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 16 t x^{3} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.106 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 16 x^{4} + 16 t x^{3} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.107 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 16 x^{4} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.108 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 8 t x^{2} + 16 t x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.153 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T694) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 24 x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.154 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T694) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 8 x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.155 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T694) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 8 x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.156 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T694) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 24 x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.161 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 8 x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.162 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 24 x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.163 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 24 x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.164 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 8 x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.205 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + 24 x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.206 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + 8 x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.207 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + 8 x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.208 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + 24 x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.233 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T690) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 16 x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.234 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T690) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(8 t + 8\right) x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.235 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T690) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.236 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8:C_8:C_4$ (as 16T690) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 16 x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 16 x + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.285 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_8:D_8$ (as 16T693) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 16 x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.286 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_8:D_8$ (as 16T693) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.287 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 x ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_8:D_8$ (as 16T693) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(8 t + 8\right) x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.288 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_8:D_8$ (as 16T693) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 16 x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.349 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_8:D_8$ (as 16T679) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + 24 x^{4} + 16 t x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.350 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_8:D_8$ (as 16T679) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + 8 x^{4} + 16 t x^{3} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.351 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_8:D_8$ (as 16T679) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + 8 x^{4} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.352 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_8:D_8$ (as 16T679) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + 24 x^{4} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.365 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_2^2$ (as 16T687) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 8 x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.366 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_2^2$ (as 16T687) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 24 x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.367 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_2^2$ (as 16T687) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 24 x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.368 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_8^2:C_2^2$ (as 16T687) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 8 x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.369 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_8:\SD_{16}$ (as 16T706) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 24 x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.370 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_8:\SD_{16}$ (as 16T706) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 8 x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.371 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_8:\SD_{16}$ (as 16T706) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 8 x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.372 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 24 ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_8:\SD_{16}$ (as 16T706) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 24 x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.409 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_8:D_8$ (as 16T679) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 8 t x^{2} + 16 t x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a3.410 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 16 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_8:D_8$ (as 16T679) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,2,\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 16 x^{4} + 8 t x^{2} + 16 t x + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 3, 7, 15]$ |
