| 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 |
| 2.4.4.44a1.109 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T841) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(8 t^{2} + 8 t\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.110 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T841) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + \left(8 t^{2} + 8 t\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.111 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T841) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.112 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T841) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + \left(8 t^{2} + 8 t\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.113 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T841) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(8 t^{2} + 8 t\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.114 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T841) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + \left(8 t^{2} + 8 t\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.115 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T841) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + \left(8 t^{2} + 8 t\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.116 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T841) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + \left(8 t^{2} + 8 t\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.311 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2).C_4$ (as 16T859) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.312 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.313 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2).C_4$ (as 16T859) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.314 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.315 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2).C_4$ (as 16T859) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.316 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.317 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2).C_4$ (as 16T859) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.318 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{3} ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.567 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2).C_4$ (as 16T859) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.568 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.569 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2).C_4$ (as 16T859) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.570 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.571 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2).C_4$ (as 16T859) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.572 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.573 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2).C_4$ (as 16T859) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.574 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2}\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t^{3} x^{2} + \left(8 t^{3} + 8 t^{2} + 8\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.983 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.984 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 24 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.985 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.986 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 24 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.987 |
$16$ |
$( x^{4} + x + 1 )^{4} + 12 ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{2} + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.988 |
$16$ |
$( x^{4} + x + 1 )^{4} + 12 ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 24 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{2} + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.989 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.990 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + 8 x^{2} ( x^{4} + x + 1 ) + 24 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1023 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{2} + 8 x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1024 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 8 x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1025 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 8 x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1026 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 8 x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1027 |
$16$ |
$( x^{4} + x + 1 )^{4} + 12 ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 8 x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1028 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 8 x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1029 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 8 x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1030 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T917) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 8 x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1083 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t^{2}\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1084 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t^{2}\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1085 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t^{2}\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1086 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t^{2}\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1087 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t^{2}\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1088 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t^{2}\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1089 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t^{2}\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1090 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 4 x^{2} + 8 x + 12\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{3} + 4 x^{2} + 4 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2\times D_4^2):C_4$ (as 16T858) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + \left(4 t^{3} + 4\right) x^{2} + \left(8 t^{3} + 8 t^{2}\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1255 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T841) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + \left(8 t^{2} + 8 t\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1256 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_2^6.C_8$ (as 16T841) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,2,2,\frac{7}{2}]$ |
$[1,1,1,1,\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 x^{2} + \left(8 t^{2} + 8 t\right) x + 24 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
