| 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 |
| 2.2.8.54a2.4377 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4378 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4379 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4380 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4381 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4382 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4383 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4384 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4561 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4562 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4563 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4564 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4565 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4566 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4567 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.4568 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6689 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 8 t x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6690 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 8 t x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6691 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6692 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6693 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 t x^{2} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6694 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6695 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 8 t x^{2} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6696 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 8 t x^{2} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6761 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 8 t x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6762 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 8 t x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6763 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 16 t x^{3} + 8 t x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6764 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6765 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 t x^{2} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6766 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 16 t x^{3} + 8 t x^{2} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6767 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 8 t x^{2} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6768 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 8 t x^{2} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6849 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6850 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6851 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 8 x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6852 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 8 x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6853 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6854 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6855 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6856 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6857 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6858 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6859 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + 2 t x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6860 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 16\right) x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6861 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6862 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6863 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.6864 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + \left(16 x + 16\right) ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,\frac{7}{2},4,\frac{9}{2}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.7033 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 8\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.7034 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 24\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(C_2\times C_4^3).D_4$ (as 16T1112) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4, \frac{9}{2}, \frac{9}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},3,\frac{7}{2},\frac{7}{2}]^{4}$ |
$[2,3,4,\frac{7}{2},\frac{9}{2}]_{2}$ |
$[1,2,3,\frac{5}{2},\frac{7}{2}]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
