| 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 |
| 2.2.8.54a2.1123 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 16\right) x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1124 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 2 t x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1127 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1128 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1129 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 16\right) x^{4} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1130 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 2 t x^{4} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1133 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1134 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1145 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 24\right) x^{4} + \left(16 t + 16\right) x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1146 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1147 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 8\right) x^{4} + 16 x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1148 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 24\right) x^{4} + 16 x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1149 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1150 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1151 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 8\right) x^{4} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1152 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 24\right) x^{4} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1153 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 2 t x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1154 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(2 t + 16\right) x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1155 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 2 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1156 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(2 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1157 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 2 t x^{4} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1158 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(2 t + 16\right) x^{4} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1159 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 2 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1160 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1315 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1316 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1319 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1320 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1321 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1322 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1325 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + 16 t x^{3} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1326 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1108) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1337 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1338 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + \left(16 t + 16\right) x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1341 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1342 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1345 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(2 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1346 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(2 t + 24\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1349 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1350 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1969 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 24\right) x^{4} + 16 x^{3} + 8 t x^{2} + \left(16 t + 16\right) x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1970 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 8\right) x^{4} + 16 x^{3} + 8 t x^{2} + \left(16 t + 16\right) x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1971 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 24\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + \left(16 t + 16\right) x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1972 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + \left(16 t + 16\right) x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1973 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 24\right) x^{4} + 8 t x^{2} + \left(16 t + 16\right) x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1974 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 8\right) x^{4} + 8 t x^{2} + \left(16 t + 16\right) x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1975 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 t x^{2} + \left(16 t + 16\right) x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1976 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + \left(16 t + 16\right) x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1977 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 24\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1978 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4^2:\OD_{16}$ (as 16T1120) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(2 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
