| 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 |
| 2.4.2.8a2.1 |
$8$ |
$( x^{4} + x + 1 )^{2} + 2 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$2$ |
$8$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{4}$ |
$[1,1,1,1]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{2} + \left(2 t^{2} + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + t$ |
$[1, 3]$ |
| 2.4.2.8a2.2 |
$8$ |
$( x^{4} + x + 1 )^{2} + 2 x ( x^{4} + x + 1 ) + 6$ |
$2$ |
$4$ |
$2$ |
$8$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{4}$ |
$[1,1,1,1]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{2} + \left(2 t^{2} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t$ |
$[1, 3]$ |
| 2.4.2.8a4.1 |
$8$ |
$( x^{4} + x + 1 )^{2} + 2 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$2$ |
$8$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{4}$ |
$[1,1,1,1]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + t^3$ |
$[1, 3]$ |
| 2.4.2.8a4.2 |
$8$ |
$( x^{4} + x + 1 )^{2} + 2 x^{3} ( x^{4} + x + 1 ) + 6$ |
$2$ |
$4$ |
$2$ |
$8$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{4}$ |
$[1,1,1,1]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t^3$ |
$[1, 3]$ |
| 2.4.2.12a1.3 |
$8$ |
$( x^{4} + x + 1 )^{2} + 4 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$2$ |
$12$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 3]^{4}$ |
$[1,1,1,2]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.4.2.12a1.4 |
$8$ |
$( x^{4} + x + 1 )^{2} + 4 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$2$ |
$12$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 3]^{4}$ |
$[1,1,1,2]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t + 4\right) x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.4.2.12a1.11 |
$8$ |
$( x^{4} + x + 1 )^{2} + \left(4 x^{3} + 4\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$2$ |
$12$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 3]^{4}$ |
$[1,1,1,2]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.4.2.12a1.12 |
$8$ |
$( x^{4} + x + 1 )^{2} + \left(4 x^{3} + 4\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$2$ |
$12$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 3]^{4}$ |
$[1,1,1,2]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t\right) x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.2.4.18a1.13 |
$8$ |
$( x^{2} + x + 1 )^{4} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$4$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, 3, \frac{7}{2}]^{4}$ |
$[1,2,2,\frac{5}{2}]^{4}$ |
$[3,3]^{2}$ |
$[2,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.2.4.18a1.14 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$4$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, 3, \frac{7}{2}]^{4}$ |
$[1,2,2,\frac{5}{2}]^{4}$ |
$[3,3]^{2}$ |
$[2,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + 2 x^{2} + 8 x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.2.4.18a1.15 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$4$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, 3, \frac{7}{2}]^{4}$ |
$[1,2,2,\frac{5}{2}]^{4}$ |
$[3,3]^{2}$ |
$[2,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 8 x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.2.4.18a1.16 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 x ( x^{2} + x + 1 )^{3} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$4$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, 3, \frac{7}{2}]^{4}$ |
$[1,2,2,\frac{5}{2}]^{4}$ |
$[3,3]^{2}$ |
$[2,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + \left(8 t + 2\right) x^{2} + 8 x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.2.4.18a1.17 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$4$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, 3, \frac{7}{2}]^{4}$ |
$[1,2,2,\frac{5}{2}]^{4}$ |
$[3,3]^{2}$ |
$[2,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 2\right) x^{2} + 8 x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.2.4.18a1.18 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$4$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, 3, \frac{7}{2}]^{4}$ |
$[1,2,2,\frac{5}{2}]^{4}$ |
$[3,3]^{2}$ |
$[2,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{2} + 8 x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.2.4.18a1.19 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$4$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, 3, \frac{7}{2}]^{4}$ |
$[1,2,2,\frac{5}{2}]^{4}$ |
$[3,3]^{2}$ |
$[2,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 2\right) x^{2} + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.2.4.18a1.20 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$4$ |
$18$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 3, 3, \frac{7}{2}]^{4}$ |
$[1,2,2,\frac{5}{2}]^{4}$ |
$[3,3]^{2}$ |
$[2,2]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 2 x^{2} + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 2, 8]$ |
| 2.2.4.20a2.13 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + 4 t x^{2} + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 3, 7]$ |
| 2.2.4.20a2.14 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{2} + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 4\right) x^{2} + 8 x + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 3, 7]$ |
| 2.2.4.20a2.15 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + 4 t x^{2} + 8 x + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 3, 7]$ |
| 2.2.4.20a2.16 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 8\right) ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 4\right) x^{2} + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 3, 7]$ |
| 2.2.4.20a2.29 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + \left(4 t + 8\right) x^{2} + 8 x + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 3, 7]$ |
| 2.2.4.20a2.30 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{2} + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + 4 t x^{2} + 8 x + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 3, 7]$ |
| 2.2.4.20a2.31 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + \left(4 t + 4\right) x^{2} + 8 x + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 3, 7]$ |
| 2.2.4.20a2.32 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + \left(4 x + 12\right) ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$20$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(4 t + 4\right) x^{3} + 4 t x^{2} + 8 t + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 3, 7]$ |
| 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) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 8 t x + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.65 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 8 t x + 24 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.66 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{2} + 8 t x + 24 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.73 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + \left(8 t + 8\right) x + 24 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.74 |
$8$ |
$( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 8\right) ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,1,2,\frac{5}{2},3]^{2}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{2} + \left(8 t + 8\right) x + 24 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.8.30a1.65 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.66 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 4 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.67 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{5} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 16 x^{5} + 4 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.68 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 16 x^{5} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 16 x^{5} + 4 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.69 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{4} + 18$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{4} + 18$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.70 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 4 x^{4} + 18$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 4 x^{4} + 18$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.71 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{5} + 4 x^{4} + 18$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 16 x^{5} + 4 x^{4} + 18$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.72 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 16 x^{5} + 4 x^{4} + 18$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 16 x^{5} + 4 x^{4} + 18$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.73 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.74 |
$8$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 4 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.75 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.76 |
$8$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 4 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.77 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 18$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 18$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.78 |
$8$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 4 x^{4} + 18$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 4 x^{4} + 18$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.79 |
$8$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 18$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 18$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.80 |
$8$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 4 x^{4} + 18$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 24 x^{6} + 16 x^{5} + 4 x^{4} + 18$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.97 |
$8$ |
$x^{8} + 8 x^{7} + 4 x^{4} + 10$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{4} + 10$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.30a1.98 |
$8$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 4 x^{4} + 10$ |
$2$ |
$1$ |
$8$ |
$30$ |
$((C_8 : C_2):C_2):C_2$ (as 8T27) |
$1$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{7} + 16 x^{6} + 4 x^{4} + 10$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
