| 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 |
| 2.2.8.32c10.3 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{9}{4}, \frac{5}{2}]^{4}$ |
$[1,1,1,1,\frac{5}{4},\frac{3}{2}]^{4}$ |
$[2,2,\frac{9}{4}]^{2}$ |
$[1,1,\frac{5}{4}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 2 x^{4} + \left(4 t + 4\right) x + 6$ |
$[9, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + (t + 1)$ |
$[1, 2, 7, 15]$ |
| 2.2.8.32c10.4 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{9}{4}, \frac{5}{2}]^{4}$ |
$[1,1,1,1,\frac{5}{4},\frac{3}{2}]^{4}$ |
$[2,2,\frac{9}{4}]^{2}$ |
$[1,1,\frac{5}{4}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + \left(4 t + 2\right) x^{4} + \left(4 t + 4\right) x + 6$ |
$[9, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + (t + 1)$ |
$[1, 2, 7, 15]$ |
| 2.2.8.32c10.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{9}{4}, \frac{5}{2}]^{4}$ |
$[1,1,1,1,\frac{5}{4},\frac{3}{2}]^{4}$ |
$[2,2,\frac{9}{4}]^{2}$ |
$[1,1,\frac{5}{4}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 2 x^{4} + \left(4 t + 4\right) x + 2$ |
$[9, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + (t + 1)$ |
$[1, 2, 7, 15]$ |
| 2.2.8.32c10.8 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$32$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, \frac{5}{2}]$ |
$[1,1,\frac{3}{2}]$ |
$[2, 2, 2, 2, \frac{9}{4}, \frac{5}{2}]^{4}$ |
$[1,1,1,1,\frac{5}{4},\frac{3}{2}]^{4}$ |
$[2,2,\frac{9}{4}]^{2}$ |
$[1,1,\frac{5}{4}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + \left(4 t + 2\right) x^{4} + \left(4 t + 4\right) x + 2$ |
$[9, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + (t + 1)$ |
$[1, 2, 7, 15]$ |
| 2.2.8.36b8.9 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$36$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, 3]$ |
$[1,1,2]$ |
$[2, 2, 2, 2, 3, 3]^{4}$ |
$[1,1,1,1,2,2]^{4}$ |
$[2,2,3]^{2}$ |
$[1,1,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + 2 t x^{6} + 2 x^{4} + 4 x^{3} + 6$ |
$[11, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.36b8.10 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 10$ |
$2$ |
$2$ |
$8$ |
$36$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, 3]$ |
$[1,1,2]$ |
$[2, 2, 2, 2, 3, 3]^{4}$ |
$[1,1,1,1,2,2]^{4}$ |
$[2,2,3]^{2}$ |
$[1,1,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 2 t x^{6} + 2 x^{4} + 4 x^{3} + 6$ |
$[11, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.36b8.29 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$8$ |
$36$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, 3]$ |
$[1,1,2]$ |
$[2, 2, 2, 2, 3, 3]^{4}$ |
$[1,1,1,1,2,2]^{4}$ |
$[2,2,3]^{2}$ |
$[1,1,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + 2 t x^{6} + 2 x^{4} + 4 x^{3} + 2$ |
$[11, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.36b8.30 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 14$ |
$2$ |
$2$ |
$8$ |
$36$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, 3]$ |
$[1,1,2]$ |
$[2, 2, 2, 2, 3, 3]^{4}$ |
$[1,1,1,1,2,2]^{4}$ |
$[2,2,3]^{2}$ |
$[1,1,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 2 t x^{6} + 2 x^{4} + 4 x^{3} + 2$ |
$[11, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + 1$ |
$[1, 2, 7, 15]$ |
| 2.2.8.36b9.13 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$36$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, 3]$ |
$[1,1,2]$ |
$[2, 2, 2, 2, 3, 3]^{4}$ |
$[1,1,1,1,2,2]^{4}$ |
$[2,2,3]^{2}$ |
$[1,1,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + \left(4 t + 4\right) x^{5} + 2 x^{4} + 4 t x^{3} + 6$ |
$[11, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + t$ |
$[1, 2, 7, 15]$ |
| 2.2.8.36b9.16 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$36$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, 3]$ |
$[1,1,2]$ |
$[2, 2, 2, 2, 3, 3]^{4}$ |
$[1,1,1,1,2,2]^{4}$ |
$[2,2,3]^{2}$ |
$[1,1,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + 2 t x^{6} + \left(4 t + 4\right) x^{5} + 2 x^{4} + 4 t x^{3} + 6$ |
$[11, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + t$ |
$[1, 2, 7, 15]$ |
| 2.2.8.36b9.35 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$8$ |
$36$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, 3]$ |
$[1,1,2]$ |
$[2, 2, 2, 2, 3, 3]^{4}$ |
$[1,1,1,1,2,2]^{4}$ |
$[2,2,3]^{2}$ |
$[1,1,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 2 t x^{6} + \left(4 t + 4\right) x^{5} + 2 x^{4} + 4 t x^{3} + 2$ |
$[11, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + t$ |
$[1, 2, 7, 15]$ |
| 2.2.8.36b9.36 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$8$ |
$36$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, 3]$ |
$[1,1,2]$ |
$[2, 2, 2, 2, 3, 3]^{4}$ |
$[1,1,1,1,2,2]^{4}$ |
$[2,2,3]^{2}$ |
$[1,1,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 2 t x^{6} + \left(4 t + 4\right) x^{5} + 2 x^{4} + 4 t x^{3} + 2$ |
$[11, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + t$ |
$[1, 2, 7, 15]$ |
| 2.2.8.36b10.11 |
$16$ |
$( x^{2} + x + 1 )^{8} + 2 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$36$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, 3]$ |
$[1,1,2]$ |
$[2, 2, 2, 2, \frac{9}{4}, 3]^{4}$ |
$[1,1,1,1,\frac{5}{4},2]^{4}$ |
$[2,2,\frac{9}{4}]^{2}$ |
$[1,1,\frac{5}{4}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + 2 t x^{6} + 4 x^{5} + 2 x^{4} + \left(4 t + 4\right) x^{3} + 6$ |
$[11, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + (t + 1)$ |
$[1, 2, 7, 15]$ |
| 2.2.8.36b10.14 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$36$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, 3]$ |
$[1,1,2]$ |
$[2, 2, 2, 2, \frac{9}{4}, 3]^{4}$ |
$[1,1,1,1,\frac{5}{4},2]^{4}$ |
$[2,2,\frac{9}{4}]^{2}$ |
$[1,1,\frac{5}{4}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 2 t x^{6} + 4 x^{5} + 2 x^{4} + \left(4 t + 4\right) x^{3} + 6$ |
$[11, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + (t + 1)$ |
$[1, 2, 7, 15]$ |
| 2.2.8.36b10.33 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$8$ |
$36$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, 3]$ |
$[1,1,2]$ |
$[2, 2, 2, 2, \frac{9}{4}, 3]^{4}$ |
$[1,1,1,1,\frac{5}{4},2]^{4}$ |
$[2,2,\frac{9}{4}]^{2}$ |
$[1,1,\frac{5}{4}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + 2 t x^{6} + 4 x^{5} + 2 x^{4} + \left(4 t + 4\right) x^{3} + 2$ |
$[11, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + (t + 1)$ |
$[1, 2, 7, 15]$ |
| 2.2.8.36b10.34 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{7} + 2 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 6$ |
$2$ |
$2$ |
$8$ |
$36$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 2, 3]$ |
$[1,1,2]$ |
$[2, 2, 2, 2, \frac{9}{4}, 3]^{4}$ |
$[1,1,1,1,\frac{5}{4},2]^{4}$ |
$[2,2,\frac{9}{4}]^{2}$ |
$[1,1,\frac{5}{4}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 2 t x^{6} + 4 x^{5} + 2 x^{4} + \left(4 t + 4\right) x^{3} + 2$ |
$[11, 6, 4, 0]$ |
$[2, 1]$ |
$z^6 + z^2 + t,t z + (t + 1)$ |
$[1, 2, 7, 15]$ |
| 2.2.8.48c13.257 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + 8 t x^{3} + \left(4 t + 4\right) x^{2} + 8 t x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.258 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + 8 t x^{3} + \left(4 t + 4\right) x^{2} + 8 t x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.259 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + 8 t x^{3} + \left(4 t + 4\right) x^{2} + 8 t x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.260 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + 8 t x^{3} + \left(4 t + 4\right) x^{2} + 8 t x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.261 |
$16$ |
$( x^{2} + x + 1 )^{8} + 6 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{5} + 2 t x^{4} + 8 t x^{3} + \left(4 t + 4\right) x^{2} + 8 t x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.262 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 8 x^{5} + 2 t x^{4} + 8 t x^{3} + \left(4 t + 4\right) x^{2} + 8 t x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.263 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{5} + 2 t x^{4} + 8 t x^{3} + \left(4 t + 4\right) x^{2} + 8 t x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.264 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 6 ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 8 x^{5} + 2 t x^{4} + 8 t x^{3} + \left(4 t + 4\right) x^{2} + 8 t x + 6$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.473 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + \left(4 t + 4\right) x^{2} + 8 t x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.474 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + \left(4 t + 4\right) x^{2} + 8 t x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.475 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + \left(4 t + 4\right) x^{2} + 8 t x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.476 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + \left(4 t + 4\right) x^{2} + 8 t x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.477 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 2 t x^{4} + \left(4 t + 4\right) x^{2} + 8 t x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.478 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 2 t x^{4} + \left(4 t + 4\right) x^{2} + 8 t x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.479 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 2 t x^{4} + \left(4 t + 4\right) x^{2} + 8 t x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.48c13.480 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 6$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]^{2}$ |
$[1,1,\frac{5}{2}]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(4 t + 4\right) x^{6} + 8 x^{5} + 2 t x^{4} + \left(4 t + 4\right) x^{2} + 8 t x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + (t + 1),(t + 1) z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1075 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(2 t + 8\right) x^{4} + 16 x^{3} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1076 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(2 t + 24\right) x^{4} + 16 x^{3} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1079 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(2 t + 8\right) x^{4} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.1080 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(2 t + 24\right) x^{4} + 16 x + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3579 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3580 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3583 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(2 t + 24\right) x^{4} + \left(16 t + 16\right) x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3584 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + \left(2 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3777 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 8\right) x^{5} + \left(2 t + 8\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3778 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 8\right) x^{5} + \left(2 t + 24\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3781 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 8\right) x^{5} + \left(2 t + 8\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3782 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 8\right) x^{5} + \left(2 t + 24\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3785 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(2 t + 16\right) x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3786 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 2 t x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3789 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(2 t + 16\right) x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.3790 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 6\right) ( x^{2} + x + 1 )^{6} + \left(4 x + 14\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 2 t x^{4} + \left(8 t + 8\right) x^{2} + 6$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.5841 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + 2 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(8 t + 8\right) x^{5} + 2 t x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
| 2.2.8.54a2.5842 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 2\right) ( x^{2} + x + 1 )^{6} + \left(12 x + 6\right) ( x^{2} + x + 1 )^{5} + \left(2 x + 16\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 6$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^2.C_2\wr C_4$ (as 16T681) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2},\frac{9}{2}]$ |
$[1,2,\frac{5}{2},\frac{7}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(8 t + 8\right) x^{5} + \left(2 t + 16\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + t,t z^2 + t,t z + t$ |
$[1, 3, 7, 15]$ |
