| 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 |
| 2.2.8.54a1.35 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.36 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + 2 x^{4} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.37 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 16 t x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.38 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + 2 x^{4} + 16 t x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.39 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.40 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + 2 x^{4} + 16 x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.41 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.42 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + 2 x^{4} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.43 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.44 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + 2 x^{4} + 16 t x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.45 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.46 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + 2 x^{4} + 16 x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.59 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.(C_4\times D_4)$ (as 16T915) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.60 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.(C_4\times D_4)$ (as 16T915) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{5} + 2 x^{4} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.61 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.(C_4\times D_4)$ (as 16T915) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 16 t x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.62 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.(C_4\times D_4)$ (as 16T915) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{5} + 2 x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.63 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.(C_4\times D_4)$ (as 16T915) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.64 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.(C_4\times D_4)$ (as 16T915) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{5} + 2 x^{4} + 16 x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.99 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.100 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + 2 x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.101 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.102 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T813) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + 2 x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.105 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.(C_4\times D_4)$ (as 16T915) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.106 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.(C_4\times D_4)$ (as 16T915) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{5} + 2 x^{4} + \left(16 t + 16\right) x^{3} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.143 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(8 t + 8\right) x^{5} + \left(24 t + 2\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.144 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(8 t + 8\right) x^{5} + \left(8 t + 2\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.145 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(8 t + 8\right) x^{5} + \left(24 t + 2\right) x^{4} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.146 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(8 t + 8\right) x^{5} + \left(8 t + 2\right) x^{4} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.147 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(8 t + 8\right) x^{5} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.148 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(8 t + 8\right) x^{5} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.149 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(8 t + 8\right) x^{5} + \left(24 t + 2\right) x^{4} + 16 x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.150 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(8 t + 8\right) x^{5} + \left(8 t + 2\right) x^{4} + 16 x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.159 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(D_4\times C_2^3).C_2^3$ (as 16T1015) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.160 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(D_4\times C_2^3).C_2^3$ (as 16T1015) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + 16 t x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.161 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(D_4\times C_2^3).C_2^3$ (as 16T1015) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.162 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(D_4\times C_2^3).C_2^3$ (as 16T1015) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.163 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(D_4\times C_2^3).C_2^3$ (as 16T1015) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.164 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(D_4\times C_2^3).C_2^3$ (as 16T1015) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.165 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(D_4\times C_2^3).C_2^3$ (as 16T1015) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + 16 x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.166 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(D_4\times C_2^3).C_2^3$ (as 16T1015) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + 16 x^{3} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.205 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.206 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.207 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + 16 x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.208 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + 16 x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.209 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.210 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + 16 t x^{3} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.211 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.212 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^5.(C_2\times D_4)$ (as 16T963) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.221 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(D_4\times C_2^3).C_2^3$ (as 16T1015) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(8 t + 2\right) x^{4} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.222 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$(D_4\times C_2^3).C_2^3$ (as 16T1015) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{2}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{2}$ |
$[3,3,4,4,\frac{17}{4}]$ |
$[2,2,3,3,\frac{13}{4}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(24 t + 2\right) x^{4} + 8 x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
