| 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 |
| 2.4.4.44a1.25 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.26 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.27 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.28 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.29 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{2} ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.30 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{2} ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.31 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.32 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.33 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.34 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.35 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.36 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.37 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.38 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.39 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.40 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.591 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T863) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 t x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.592 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T863) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.593 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T863) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.594 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T863) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.595 |
$16$ |
$( x^{4} + x + 1 )^{4} + 12 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T863) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.596 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T863) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.597 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T863) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.598 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T863) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.655 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T939) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 t x^{2} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.656 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T863) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t x^{2} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.657 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T939) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t x^{2} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.658 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T863) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t x^{2} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.659 |
$16$ |
$( x^{4} + x + 1 )^{4} + 12 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T939) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t x^{2} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.660 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T863) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t x^{2} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.661 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T939) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.662 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T863) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1167 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1168 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1169 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 x^{2} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1170 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 x^{2} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1171 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{2} ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 4 x^{2} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1172 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{2} ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 4 x^{2} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1173 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 4 x^{2} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1174 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 4 x^{2} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1175 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 x^{2} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1176 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 x^{2} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1177 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 x^{2} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1178 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 x^{2} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1179 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 4 x^{2} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1180 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 4 x^{2} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1181 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6:(C_2\times C_4)$ (as 16T815) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 x^{2} + 8 t x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1182 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T820) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 x^{2} + 8 t x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1675 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{4} + x + 1 )^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T939) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t x^{2} + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1676 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x + 4\right) ( x^{4} + x + 1 )^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^3\wr C_2:C_4$ (as 16T939) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t x^{2} + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
