| 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 |
| 2.2.8.54a2.9 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.10 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.13 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.14 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 2 t x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.19 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_4$ (as 16T694) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.20 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_4$ (as 16T694) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.23 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_4$ (as 16T694) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 2 t x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.24 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_4$ (as 16T694) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.195 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.196 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.199 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.200 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.201 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8:C_8:C_4$ (as 16T690) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.202 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8:C_8:C_4$ (as 16T690) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.205 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8:C_8:C_4$ (as 16T690) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.206 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8:C_8:C_4$ (as 16T690) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.369 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:\SD_{16}$ (as 16T706) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 18\right) x^{4} + 16 x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.370 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:\SD_{16}$ (as 16T706) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.373 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:\SD_{16}$ (as 16T706) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 18\right) x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.374 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:\SD_{16}$ (as 16T706) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.443 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:D_8$ (as 16T679) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 16 x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.444 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:D_8$ (as 16T679) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 16 x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.447 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:D_8$ (as 16T679) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.448 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:D_8$ (as 16T679) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.537 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:D_8$ (as 16T679) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.538 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:D_8$ (as 16T679) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.541 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:D_8$ (as 16T679) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.542 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:D_8$ (as 16T679) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.547 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:D_8$ (as 16T693) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.548 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:D_8$ (as 16T693) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.551 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:D_8$ (as 16T693) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 16 x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.552 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:D_8$ (as 16T693) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 16 x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.723 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:\SD_{16}$ (as 16T706) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.724 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:\SD_{16}$ (as 16T706) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.727 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:\SD_{16}$ (as 16T706) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.728 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:\SD_{16}$ (as 16T706) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.729 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_2^2$ (as 16T687) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.730 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_2^2$ (as 16T687) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 18\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.733 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_2^2$ (as 16T687) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.734 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_2^2$ (as 16T687) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 18\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.889 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 16 x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.890 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 16 x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.893 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.894 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8^2:C_4$ (as 16T664) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.963 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 2 t x^{4} + \left(16 t + 16\right) x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.964 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.967 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 2 t x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.968 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_8:C_8:C_4$ (as 16T668) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1075 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(2 t + 8\right) x^{4} + 16 x^{3} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1076 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(2 t + 24\right) x^{4} + 16 x^{3} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
