| 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 |
| 2.2.8.54a1.2285 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2286 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 8 t x^{5} + 2 x^{4} + 16 x^{3} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2287 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2288 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 8 t x^{5} + 2 x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2289 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2290 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 8 t x^{5} + 2 x^{4} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2291 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2292 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 8 t x^{5} + 2 x^{4} + 16 t x^{3} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2293 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 28\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 2\right) x^{4} + 16 t x^{3} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2294 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 28\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 16 t x^{3} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2295 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 28\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2296 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 28\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 2\right) x^{4} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2297 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 28\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2298 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 28\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + \left(16 t + 16\right) x^{3} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2299 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 28\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 16 x^{3} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2300 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 28\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2357 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 2 x^{4} + 16 x^{3} + 16 x + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2358 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 16 x + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2359 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2360 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 2 x^{4} + \left(16 t + 16\right) x^{3} + 16 x + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2361 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 2 x^{4} + 16 x + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2362 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 16 x + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2363 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 16 t x^{3} + 16 x + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2364 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 4 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 2 x^{4} + 16 t x^{3} + 16 x + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2553 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 8\right) x^{5} + \left(8 t + 2\right) x^{4} + 16 x^{3} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2554 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + \left(8 t + 8\right) x^{5} + \left(24 t + 2\right) x^{4} + 16 x^{3} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2567 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 16 t x^{3} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2568 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2569 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 2\right) x^{4} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2570 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2571 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2572 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2573 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 2\right) x^{4} + 16 x^{3} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2574 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 16 x^{3} + 8 t x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2663 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + 16 t x^{3} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2664 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + 16 t x^{3} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2665 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2666 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2667 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2668 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2669 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(8 t + 2\right) x^{4} + 16 x^{3} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2670 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 x^{6} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + 16 x^{3} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2687 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2688 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2689 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(8 t + 2\right) x^{4} + 16 x^{3} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2690 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(24 t + 2\right) x^{4} + 16 x^{3} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2691 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(24 t + 2\right) x^{4} + 16 t x^{3} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2692 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(8 t + 2\right) x^{4} + 16 t x^{3} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2693 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(8 t + 2\right) x^{4} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.54a1.2694 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{3} + 12 ( x^{2} + x + 1 )^{2} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_2^4.C_2\wr C_4$ (as 16T1251) |
$4$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 3, 3, \frac{7}{2}, 4, 4, \frac{17}{4}, \frac{9}{2}]^{4}$ |
$[1,2,2,\frac{5}{2},3,3,\frac{13}{4},\frac{7}{2}]^{4}$ |
$[\frac{17}{4},3,3,4,4]_{2}$ |
$[\frac{13}{4},2,2,3,3]_{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(24 t + 2\right) x^{4} + 8 x^{2} + 4 t + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
