| 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 |
| 2.2.8.54a2.377 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.378 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.379 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + 16 x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.380 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + 16 x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.381 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.382 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.383 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.384 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.425 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.426 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.427 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.428 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.429 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.430 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.431 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 16 x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.432 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 16 x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.449 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.450 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 16 t x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.451 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.452 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.453 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.454 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.455 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 16 x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.456 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 16 x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.497 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 2 t x^{4} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.498 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.499 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 2 t x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.500 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.501 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 16 x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.502 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 16 x^{3} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.503 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.504 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 8 x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.521 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.522 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 2 t x^{4} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.523 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.524 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.525 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.526 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 2 t x^{4} + 16 x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.527 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.528 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.529 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.530 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 16 t x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.531 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 2 t x^{4} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.532 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.533 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + \left(2 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.534 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.535 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 2 t x^{4} + 16 x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.536 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2},\frac{7}{2},\frac{9}{2}]^{2}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 2 t x^{4} + 16 x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.553 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 16 x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.554 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^7.D_4:D_4$ (as 16T1713) |
not computed |
not computed |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
not computed |
not computed |
not computed |
not computed |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 2 t x^{4} + 16 x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
