| 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 |
| 2.2.8.56a1.372 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$Q_8^2:C_4$ (as 16T704) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.373 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$Q_8^2:C_4$ (as 16T704) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.374 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$Q_8^2:C_4$ (as 16T704) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.375 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$Q_8^2:C_4$ (as 16T704) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.419 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T658) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.420 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T658) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.421 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T658) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.422 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T658) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.423 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T658) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.424 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T658) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.425 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T658) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.426 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T658) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.443 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.444 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.445 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.446 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.463 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$Q_8^2:C_4$ (as 16T704) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.464 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$Q_8^2:C_4$ (as 16T704) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.465 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$Q_8^2:C_4$ (as 16T704) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.466 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$Q_8^2:C_4$ (as 16T704) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.475 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T683) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.476 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T683) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x^{3} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.477 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T683) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.478 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T683) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.510 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.511 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.512 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.513 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.525 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T683) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.526 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T683) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.527 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T683) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.528 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T683) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.557 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T658) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.558 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T658) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.559 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 4 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T658) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.560 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + 20 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$(C_4\times C_8).D_4$ (as 16T658) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.585 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$Q_8^2:C_4$ (as 16T704) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.586 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$Q_8^2:C_4$ (as 16T704) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.587 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$Q_8^2:C_4$ (as 16T704) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 20 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.588 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$Q_8^2:C_4$ (as 16T704) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + 4 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.625 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.626 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.627 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 t x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.628 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 t x^{3} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.669 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.670 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.671 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 12 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.672 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{5} + 28 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$D_4^2:C_4$ (as 16T688) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.1181 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$Q_8^2:C_4$ (as 16T704) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 12 t x^{4} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.1182 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{5} + \left(20 x + 4\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$Q_8^2:C_4$ (as 16T704) |
$4$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{4}$ |
$[2,3,4]^{2}$ |
$[1,2,3]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 28 t x^{4} + 8 x^{2} + 8 t + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
