| Label |
$n$ |
Polynomial |
$p$ |
$f$ |
$e$ |
$c$ |
Galois group |
$u$ |
$t$ |
Visible Artin slopes |
Visible Swan slopes |
Artin slope content |
Swan slope content |
Hidden Artin slopes |
Hidden Swan slopes |
$\#\Aut(K/\Q_p)$ |
Unram. Ext. |
Eisen. Poly. |
Ind. of Insep. |
Assoc. Inertia |
Resid. Poly |
Jump Set |
| 2.4.4.44a1.159 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 t^{3} x^{2} + 8 t^{3} x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.160 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.161 |
$16$ |
$( x^{4} + x + 1 )^{4} + 12 x^{2} ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.162 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.163 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.164 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.165 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(12 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.166 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.343 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.344 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.345 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.346 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.347 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.348 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.349 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.350 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.527 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.528 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.529 |
$16$ |
$( x^{4} + x + 1 )^{4} + 12 x^{2} ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.530 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2}\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.531 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.532 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.533 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(12 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.534 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.559 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.560 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.561 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.562 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 t^{3} x^{2} + 8 t^{3} x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.563 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.564 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.565 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.566 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.791 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.792 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.793 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.794 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.795 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.796 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.797 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 t^{3} x^{2} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.798 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 t^{3} x^{2} + 8 t^{3} x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.831 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.832 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.833 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(12 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.834 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.835 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.836 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.837 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(12 x^{2} + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.838 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12 x^{2} + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1091 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1092 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1269) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, \frac{5}{2}, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,\frac{3}{2},2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{5}{2},\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{3}{2},\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
