| 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 |
| 2.1.8.31a1.1 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 34$ |
$2$ |
$1$ |
$8$ |
$31$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 34$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.2 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$Z_8 : Z_8^\times$ (as 8T15) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]^{2}$ |
$[1,2,3,4]^{2}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.3 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 34$ |
$2$ |
$1$ |
$8$ |
$31$ |
$Z_8 : Z_8^\times$ (as 8T15) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]^{2}$ |
$[1,2,3,4]^{2}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 34$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.4 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 34$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 34$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.5 |
$8$ |
$x^{8} + 8 x^{6} + 34$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 34$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.6 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x + 34$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x + 34$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.7 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x + 34$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x + 34$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.8 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.9 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.10 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 34$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 34$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.11 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 34$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 34$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.12 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.13 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$Z_8 : Z_8^\times$ (as 8T15) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]^{2}$ |
$[1,2,3,4]^{2}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.14 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$Z_8 : Z_8^\times$ (as 8T15) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]^{2}$ |
$[1,2,3,4]^{2}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{3} + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.15 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.16 |
$8$ |
$x^{8} + 8 x^{6} + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.17 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.18 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.19 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.20 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.21 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.22 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 16 x + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.23 |
$8$ |
$x^{8} + 8 x^{6} + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.24 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.25 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.26 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 34$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 34$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.27 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.28 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 34$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 34$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.29 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.30 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.31 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x + 2$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.32 |
$8$ |
$x^{8} + 8 x^{6} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.33 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.34 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.35 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.36 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.37 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_4\wr C_2$ (as 8T17) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, 5]$ |
$[1,2,\frac{5}{2},3,4]$ |
$[2,\frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$4$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.38 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$D_{8}$ (as 8T6) |
$1$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2]$ |
$[1]$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x^{3} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.39 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{6} + 16 x^{5} + 16 x + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.40 |
$8$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{6} + 16 x^{5} + 16 x + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.41 |
$8$ |
$x^{8} + 16 x^{5} + 16 x^{3} + 8 x^{2} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{5} + 16 x^{3} + 8 x^{2} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.42 |
$8$ |
$x^{8} + 16 x^{5} + 16 x^{3} + 8 x^{2} + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{5} + 16 x^{3} + 8 x^{2} + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.43 |
$8$ |
$x^{8} + 16 x^{7} + 16 x^{5} + 16 x^{3} + 8 x^{2} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 16 x^{5} + 16 x^{3} + 8 x^{2} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.44 |
$8$ |
$x^{8} + 16 x^{7} + 16 x^{5} + 16 x^{3} + 8 x^{2} + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 16 x^{5} + 16 x^{3} + 8 x^{2} + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.45 |
$8$ |
$x^{8} + 16 x^{7} + 16 x^{5} + 8 x^{2} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 16 x^{5} + 8 x^{2} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.46 |
$8$ |
$x^{8} + 16 x^{5} + 8 x^{2} + 18$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{5} + 8 x^{2} + 18$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.47 |
$8$ |
$x^{8} + 16 x^{5} + 8 x^{2} + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{5} + 8 x^{2} + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.48 |
$8$ |
$x^{8} + 16 x^{7} + 16 x^{5} + 8 x^{2} + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$C_2 \wr C_2\wr C_2$ (as 8T35) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]^{2}$ |
$[1,\frac{5}{2},\frac{13}{4}]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 16 x^{5} + 8 x^{2} + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.49 |
$8$ |
$x^{8} + 16 x^{7} + 8 x^{2} + 16 x + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$D_{8}$ (as 8T6) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 16 x^{7} + 8 x^{2} + 16 x + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.8.31a1.50 |
$8$ |
$x^{8} + 8 x^{2} + 16 x + 50$ |
$2$ |
$1$ |
$8$ |
$31$ |
$D_{8}$ (as 8T6) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{8} + 8 x^{2} + 16 x + 50$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
