| 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 |
| 2.4.4.44a1.383 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.384 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.385 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{2} ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.386 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.387 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.388 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.389 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.390 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.391 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.392 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.393 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.394 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.395 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.396 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.397 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.398 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.455 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.456 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.457 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{2} ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.458 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.459 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.460 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.461 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.462 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.463 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.464 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.465 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.466 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.467 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.468 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.469 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.470 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.639 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.640 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.641 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.642 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.643 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.644 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.645 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.646 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.647 |
$16$ |
$( x^{4} + x + 1 )^{4} + 12 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.648 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.649 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.650 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.651 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.652 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.653 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.654 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.\OD_{16}$ (as 16T1150) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.711 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.712 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4\right) ( x^{4} + x + 1 )^{3} + 4 x ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^4.C_2\wr C_4$ (as 16T1239) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},3]^{4}$ |
$[2,2,2,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,1,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + \left(8 t^{2} + 8 t\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
