| 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 |
| 2.2.8.54a2.1449 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1450 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 16\right) x^{4} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1453 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 2 t x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1454 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(2 t + 16\right) x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1523 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1524 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1527 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(2 t + 8\right) x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1528 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(2 t + 24\right) x^{4} + \left(8 t + 8\right) x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1691 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 24\right) x^{4} + \left(16 t + 16\right) x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1692 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 8\right) x^{4} + \left(16 t + 16\right) x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1693 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 24\right) x^{4} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1694 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 8\right) x^{4} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1881 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{4} + \left(16 t + 16\right) x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1882 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 16\right) x^{4} + \left(16 t + 16\right) x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1887 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{4} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1888 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 16\right) x^{4} + 16 t x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3177 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3178 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3183 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(2 t + 24\right) x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3184 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(2 t + 8\right) x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3377 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3378 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(2 t + 16\right) x^{4} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3383 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(2 t + 16\right) x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3384 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 2 t x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4107 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4108 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{4} + 16 t x^{3} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4109 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4110 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4187 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4188 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4189 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4190 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.6817 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{6} + 4 t x^{4} + 8 x^{2} + 16 x + 8 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.6818 |
$16$ |
$( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 16 t x^{7} + \left(8 t + 8\right) x^{6} + 4 t x^{4} + 8 x^{2} + 16 x + 8 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.6819 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 16 t x^{7} + \left(8 t + 8\right) x^{6} + \left(16 t + 16\right) x^{5} + 4 t x^{4} + 8 x^{2} + 16 x + 40 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.6820 |
$16$ |
$( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{6} + \left(16 t + 16\right) x^{5} + 4 t x^{4} + 8 x^{2} + 16 x + 40 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.7009 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 16 t x^{7} + 8 x^{6} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 40 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.7010 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{6} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 40 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.7011 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{6} + \left(16 t + 16\right) x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.7012 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 16 t x^{7} + 8 x^{6} + \left(16 t + 16\right) x^{5} + 4 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.7145 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 16 t x^{7} + 8 t x^{6} + 4 t x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 40 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.7146 |
$16$ |
$( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{6} + 4 t x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 40 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.7147 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{6} + \left(16 t + 16\right) x^{5} + 4 t x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.7148 |
$16$ |
$( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 12 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 16 t x^{7} + 8 t x^{6} + \left(16 t + 16\right) x^{5} + 4 t x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.7261 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.7262 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{6} + \left(24 x + 12\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 16 t x^{7} + 4 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.7263 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 16 t x^{7} + \left(16 t + 16\right) x^{5} + 4 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 40 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.7264 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(16 t + 16\right) x^{5} + 4 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 40 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.15165 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 16 t x^{7} + 8 t x^{6} + 4 t x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.15166 |
$16$ |
$( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 28\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + \left(16 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_4^3.D_4$ (as 16T974) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, 5]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},4]^{2}$ |
$[2,2,\frac{7}{2},\frac{7}{2},\frac{9}{2}]$ |
$[1,1,\frac{5}{2},\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{6} + 4 t x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 8 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
