| 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 |
| 2.4.2.8a3.2 |
$8$ |
$( x^{4} + x + 1 )^{2} + \left(2 x^{2} + 2 x\right) ( x^{4} + x + 1 ) + 4 x + 2$ |
$2$ |
$4$ |
$2$ |
$8$ |
$C_8:C_2$ (as 8T7) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{4}$ |
$[1,1]^{4}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{2} + \left(2 t^{2} + 2 t + 2\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + t)$ |
$[1, 3]$ |
| 2.4.2.12a1.8 |
$8$ |
$( x^{4} + x + 1 )^{2} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$2$ |
$12$ |
$C_8:C_2$ (as 8T7) |
$4$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 3]^{4}$ |
$[1,2]^{4}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{2} + \left(4 t^{2} + 4 t + 4\right) x + 8 t^{3} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.2.4.16b2.7 |
$8$ |
$( x^{2} + x + 1 )^{4} + 2 ( x^{2} + x + 1 )^{2} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$4$ |
$16$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3, 3]^{2}$ |
$[1,2,2]^{2}$ |
$[3]$ |
$[2]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 4 t x + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 8]$ |
| 2.2.4.16b2.8 |
$8$ |
$( x^{2} + x + 1 )^{4} + 2 ( x^{2} + x + 1 )^{2} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 4 x + 10$ |
$2$ |
$2$ |
$4$ |
$16$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3, 3]^{2}$ |
$[1,2,2]^{2}$ |
$[3]$ |
$[2]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 4 t x + 4 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 8]$ |
| 2.2.4.16b2.11 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$4$ |
$16$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3, 3]^{2}$ |
$[1,2,2]^{2}$ |
$[3]$ |
$[2]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + 2 x^{2} + 4 t x + 4 t + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 8]$ |
| 2.2.4.16b2.12 |
$8$ |
$( x^{2} + x + 1 )^{4} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{3} + 2 ( x^{2} + x + 1 )^{2} + \left(4 x + 4\right) ( x^{2} + x + 1 ) + 4 x + 10$ |
$2$ |
$2$ |
$4$ |
$16$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3, 3]^{2}$ |
$[1,2,2]^{2}$ |
$[3]$ |
$[2]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 4 t x^{3} + 2 x^{2} + 4 t x + 4 t + 10$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + t$ |
$[1, 2, 8]$ |
| 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) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{4}$ |
$[2,3]^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 8 t x^{3} + 8 x + 24 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.67 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 8 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 8 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.4.22a1.68 |
$8$ |
$( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 8 ( x^{2} + x + 1 ) + 24 x + 2$ |
$2$ |
$2$ |
$4$ |
$22$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 24 t + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.1.8.31a1.147 |
$8$ |
$x^{8} + 4 x^{4} + 16 x^{3} + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 4 x^{4} + 16 x^{3} + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.148 |
$8$ |
$x^{8} + 16 x^{7} + 4 x^{4} + 16 x^{3} + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 4 x^{4} + 16 x^{3} + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.149 |
$8$ |
$x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.150 |
$8$ |
$x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.157 |
$8$ |
$x^{8} + 4 x^{4} + 16 x^{3} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 4 x^{4} + 16 x^{3} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.158 |
$8$ |
$x^{8} + 16 x^{7} + 4 x^{4} + 16 x^{3} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 4 x^{4} + 16 x^{3} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.159 |
$8$ |
$x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.160 |
$8$ |
$x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.165 |
$8$ |
$x^{8} + 8 x^{6} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 4 x^{4} + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.166 |
$8$ |
$x^{8} + 8 x^{6} + 4 x^{4} + 34$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 4 x^{4} + 34$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.177 |
$8$ |
$x^{8} + 8 x^{6} + 4 x^{4} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 4 x^{4} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.178 |
$8$ |
$x^{8} + 8 x^{6} + 4 x^{4} + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 4 x^{4} + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.223 |
$8$ |
$x^{8} + 4 x^{4} + 16 x^{3} + 10$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 4 x^{4} + 16 x^{3} + 10$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.224 |
$8$ |
$x^{8} + 4 x^{4} + 16 x^{3} + 42$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 4 x^{4} + 16 x^{3} + 42$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.235 |
$8$ |
$x^{8} + 4 x^{4} + 16 x^{3} + 26$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 4 x^{4} + 16 x^{3} + 26$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.236 |
$8$ |
$x^{8} + 4 x^{4} + 16 x^{3} + 58$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 4 x^{4} + 16 x^{3} + 58$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.245 |
$8$ |
$x^{8} + 8 x^{6} + 4 x^{4} + 10$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 4 x^{4} + 10$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.246 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 4 x^{4} + 10$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 4 x^{4} + 10$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.247 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 10$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 10$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.248 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 10$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 10$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.255 |
$8$ |
$x^{8} + 8 x^{6} + 4 x^{4} + 26$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 4 x^{4} + 26$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.256 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 4 x^{4} + 26$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 4 x^{4} + 26$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.257 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 26$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 26$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.258 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 26$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 4 x^{4} + 26$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 3.2.4.6a1.1 |
$8$ |
$( x^{2} + 2 x + 2 )^{4} + 3 x$ |
$3$ |
$2$ |
$4$ |
$6$ |
$C_8:C_2$ (as 8T7) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$[\ ]_{4}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 2 t + 2$ |
$x^{4} + 3 t$ |
$[0]$ |
$[1]$ |
$z^3 + z^2 + 1$ |
undefined |
| 5.1.8.7a1.1 |
$8$ |
$x^{8} + 5$ |
$5$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 3$ |
$x^{8} + 5$ |
$[0]$ |
$[2]$ |
$z^7 + 3 z^6 + 3 z^5 + z^4 + z^2 + 3 z + 3$ |
$[2]$ |
| 5.1.8.7a1.2 |
$8$ |
$x^{8} + 10$ |
$5$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 3$ |
$x^{8} + 10$ |
$[0]$ |
$[2]$ |
$z^7 + 3 z^6 + 3 z^5 + z^4 + z^2 + 3 z + 3$ |
undefined |
| 5.1.8.7a1.3 |
$8$ |
$x^{8} + 15$ |
$5$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 3$ |
$x^{8} + 15$ |
$[0]$ |
$[2]$ |
$z^7 + 3 z^6 + 3 z^5 + z^4 + z^2 + 3 z + 3$ |
undefined |
| 5.1.8.7a1.4 |
$8$ |
$x^{8} + 20$ |
$5$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 3$ |
$x^{8} + 20$ |
$[0]$ |
$[2]$ |
$z^7 + 3 z^6 + 3 z^5 + z^4 + z^2 + 3 z + 3$ |
undefined |
| 7.2.4.6a1.1 |
$8$ |
$( x^{2} + 6 x + 3 )^{4} + 7 x$ |
$7$ |
$2$ |
$4$ |
$6$ |
$C_8:C_2$ (as 8T7) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$[\ ]_{4}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 6 t + 3$ |
$x^{4} + 35 t + 28$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 11.2.4.6a1.1 |
$8$ |
$( x^{2} + 7 x + 2 )^{4} + 11 x$ |
$11$ |
$2$ |
$4$ |
$6$ |
$C_8:C_2$ (as 8T7) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$[\ ]_{4}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 7 t + 2$ |
$x^{4} + 33 t + 33$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 13.1.8.7a1.1 |
$8$ |
$x^{8} + 13$ |
$13$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 11$ |
$x^{8} + 13$ |
$[0]$ |
$[2]$ |
$z^7 + 8 z^6 + 2 z^5 + 4 z^4 + 5 z^3 + 4 z^2 + 2 z + 8$ |
undefined |
| 13.1.8.7a1.2 |
$8$ |
$x^{8} + 26$ |
$13$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 11$ |
$x^{8} + 26$ |
$[0]$ |
$[2]$ |
$z^7 + 8 z^6 + 2 z^5 + 4 z^4 + 5 z^3 + 4 z^2 + 2 z + 8$ |
undefined |
| 13.1.8.7a1.3 |
$8$ |
$x^{8} + 52$ |
$13$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 11$ |
$x^{8} + 52$ |
$[0]$ |
$[2]$ |
$z^7 + 8 z^6 + 2 z^5 + 4 z^4 + 5 z^3 + 4 z^2 + 2 z + 8$ |
undefined |
| 13.1.8.7a1.4 |
$8$ |
$x^{8} + 104$ |
$13$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 11$ |
$x^{8} + 104$ |
$[0]$ |
$[2]$ |
$z^7 + 8 z^6 + 2 z^5 + 4 z^4 + 5 z^3 + 4 z^2 + 2 z + 8$ |
undefined |
| 19.2.4.6a1.1 |
$8$ |
$( x^{2} + 18 x + 2 )^{4} + 19 x$ |
$19$ |
$2$ |
$4$ |
$6$ |
$C_8:C_2$ (as 8T7) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$[\ ]_{4}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 18 t + 2$ |
$x^{4} + 342 t + 323$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 23.2.4.6a1.1 |
$8$ |
$( x^{2} + 21 x + 5 )^{4} + 23 x$ |
$23$ |
$2$ |
$4$ |
$6$ |
$C_8:C_2$ (as 8T7) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$[\ ]_{4}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t^{2} + 21 t + 5$ |
$x^{4} + 23 t$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 29.1.8.7a1.1 |
$8$ |
$x^{8} + 29$ |
$29$ |
$1$ |
$8$ |
$7$ |
$C_8:C_2$ (as 8T7) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 27$ |
$x^{8} + 29$ |
$[0]$ |
$[2]$ |
$z^7 + 8 z^6 + 28 z^5 + 27 z^4 + 12 z^3 + 27 z^2 + 28 z + 8$ |
undefined |
