| 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 |
| 2.2.4.22a1.1 |
$8$ |
$( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.2 |
$8$ |
$( x^{2} + x + 1 )^{4} + 16 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$Q_8:C_2$ (as 8T11) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 16 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.3 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$Q_8:C_2$ (as 8T11) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.4 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 16 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$D_4\times C_2$ (as 8T9) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + 16 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.5 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.6 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.7 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.8 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T31) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.9 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{2}$ |
$[2,3]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.10 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 16 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$Q_8$ (as 8T5) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{2}$ |
$[2,3]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x + 16 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.11 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$Q_8:C_2$ (as 8T11) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.12 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 16 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$Q_8:C_2$ (as 8T11) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 8 x + 16 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.13 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$D_4$ (as 8T4) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{2}$ |
$[2,3]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.14 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 ) + 16 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$Q_8$ (as 8T5) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{2}$ |
$[2,3]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 8 x + 16 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.15 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 8 x + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.16 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$C_8:C_2$ (as 8T7) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{4}$ |
$[2,3]^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 8 x + 24 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.17 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.18 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$C_8:C_2$ (as 8T7) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{4}$ |
$[2,3]^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + 8 x + 24 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.19 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 8 t x + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.20 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(8 t + 8\right) x + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.21 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.22 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 8 t x + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.23 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(C_8:C_2):C_2$ (as 8T16) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 4]^{2}$ |
$[1,1,2,3]^{2}$ |
$[2,2]$ |
$[1,1]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.24 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 ) + 24 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(C_8:C_2):C_2$ (as 8T16) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 4]^{2}$ |
$[1,1,2,3]^{2}$ |
$[2,2]$ |
$[1,1]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 24 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.25 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + \left(4 t + 4\right) x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.26 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 16 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{2} + 16 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.27 |
$8$ |
$( x^{2} + x + 1 )^{4} + 12 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.28 |
$8$ |
$( x^{2} + x + 1 )^{4} + 12 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 16 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t x^{2} + 16 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.29 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 3, 4]^{4}$ |
$[1,2,2,3]^{4}$ |
$[2,3]^{2}$ |
$[1,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.30 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 3, 4]^{4}$ |
$[1,2,2,3]^{4}$ |
$[2,3]^{2}$ |
$[1,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t x^{2} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.31 |
$8$ |
$( x^{2} + x + 1 )^{4} + 12 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 3, 4]^{4}$ |
$[1,2,2,3]^{4}$ |
$[2,3]^{2}$ |
$[1,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t x^{2} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.32 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T30) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 3, 4]^{4}$ |
$[1,2,2,3]^{4}$ |
$[2,3]^{2}$ |
$[1,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{2} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.33 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + \left(4 t + 4\right) x^{2} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.34 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.35 |
$8$ |
$( x^{2} + x + 1 )^{4} + 12 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{2} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.36 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.37 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + \left(8 x + 8\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$QD_{16}$ (as 8T8) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[2]$ |
$[1]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(4 t + 4\right) x^{2} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.38 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + \left(8 x + 8\right) ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$QD_{16}$ (as 8T8) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[2]$ |
$[1]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{2} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.39 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 8 x + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.40 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + \left(4 t + 4\right) x^{2} + 8 x + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.41 |
$8$ |
$( x^{2} + x + 1 )^{4} + 12 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(4 t + 4\right) x^{2} + 8 x + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.42 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T29) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{2} + 8 x + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.43 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$Z_8 : Z_8^\times$ (as 8T15) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 4]^{2}$ |
$[1,1,2,3]^{2}$ |
$[2,2]$ |
$[1,1]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{2} + 8 t x + 24 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.44 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 24 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$Z_8 : Z_8^\times$ (as 8T15) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 4]^{2}$ |
$[1,1,2,3]^{2}$ |
$[2,2]$ |
$[1,1]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{2} + 8 t x + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.45 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$Z_8 : Z_8^\times$ (as 8T15) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 4]^{2}$ |
$[1,1,2,3]^{2}$ |
$[2,2]$ |
$[1,1]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t x^{2} + \left(8 t + 8\right) x + 24 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.46 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 24 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$Z_8 : Z_8^\times$ (as 8T15) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 4]^{2}$ |
$[1,1,2,3]^{2}$ |
$[2,2]$ |
$[1,1]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(4 t + 4\right) x^{2} + 8 t x + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.47 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{2} + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.48 |
$8$ |
$( x^{2} + x + 1 )^{4} + 12 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$(((C_4 \times C_2): C_2):C_2):C_2$ (as 8T28) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + \left(4 t + 4\right) x^{2} + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.49 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{2}$ |
$[2,3]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.50 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 16 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$C_4\times C_2$ (as 8T2) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{2}$ |
$[2,3]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$8$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{2} + 16 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
