| 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 |
| 2.2.8.54a1.1 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T111) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{4} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.2 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T111) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + \left(16 t + 2\right) x^{4} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.5 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T111) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{4} + 16 x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.6 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T111) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T107) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{4} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T107) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(16 t + 2\right) x^{4} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.11 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T107) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.12 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T107) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.175 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T114) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.176 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T114) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.179 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T114) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.180 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T114) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.181 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T113) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + 8 x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.182 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T113) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + 8 x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.185 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T113) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + 16 x^{3} + 8 x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.186 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T113) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + 16 x^{3} + 8 x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.625 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4:D_4$ (as 16T141) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.626 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4.D_4$ (as 16T137) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.627 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4.D_4$ (as 16T137) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + 16 x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.628 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4:D_4$ (as 16T141) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + 16 x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.629 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4.D_4$ (as 16T137) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.630 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4:D_4$ (as 16T141) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.633 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4:D_4$ (as 16T141) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.634 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4.D_4$ (as 16T137) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.983 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T138) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.984 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4.D_4$ (as 16T164) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 2 x^{4} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.987 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_4.D_4$ (as 16T164) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.988 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T138) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 2 x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1182 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T111) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1183 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T111) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1186 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T111) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 16 x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1187 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T111) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1190 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T107) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 16 t x^{3} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1191 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T107) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + 16 t x^{3} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1194 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T107) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 2 x^{4} + \left(16 t + 16\right) x^{3} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1195 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T107) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1196 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T111) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1197 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T111) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1200 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T111) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 16 x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1201 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2:C_2^2$ (as 16T111) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1232 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T114) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1233 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T114) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1234 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T114) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1235 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T114) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1236 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T113) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + 16 x^{3} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1237 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T113) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + 16 x^{3} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1240 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T113) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1241 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T113) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + 16 x^{3} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1246 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T114) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1247 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$D_8:C_4$ (as 16T114) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[3,4]$ |
$[2,3]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
