| 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 |
| 2.2.8.48c3.253 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.254 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 2 x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.255 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 18$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 2 x^{4} + \left(8 t + 8\right) x^{3} + \left(4 t + 4\right) x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.256 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 8 x^{5} + 2 x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.257 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 18$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 8 x^{5} + 2 x^{4} + \left(8 t + 8\right) x^{3} + \left(4 t + 4\right) x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.258 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 2 x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 26$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.259 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 26$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.260 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 2 x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.263 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 8 t x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.264 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 18$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.265 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 26$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.266 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.269 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.270 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.271 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 18$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 10$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.272 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 26$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.293 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 2 x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.294 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 26$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 8 x^{5} + 2 x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.295 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 2 x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.296 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 2 x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 18$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.297 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{5} + 2 x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.298 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 26$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 2 x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.299 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 2 x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 18$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.300 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 2 x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.303 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 18$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.304 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.305 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 26$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 8 t x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.306 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.309 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.310 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 26$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.311 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.48c3.312 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4, 4]^{2}$ |
$[1,1,2,2,3,3]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 4 t x^{2} + 8 x + 18$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.177 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + 16 x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.178 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + 16 x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.183 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.184 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + 16 t x^{3} + 8 x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.187 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.188 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1230 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + 16 x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1231 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + 16 x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1238 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1239 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1242 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + 16 t x^{3} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1243 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + 16 t x^{3} + \left(16 t + 16\right) x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1244 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(8 t + 2\right) x^{4} + 16 x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1245 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + 8 x^{5} + \left(24 t + 2\right) x^{4} + 16 x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1622 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1623 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.56a1.811 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.56a1.812 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(24 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$56$ |
$C_4^2.D_4$ (as 16T321) |
$2$ |
$1$ |
$[3, \frac{7}{2}, \frac{9}{2}]$ |
$[2,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(24 t + 4\right) x^{4} + 8 t x^{2} + 2$ |
$[21, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
