| 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 |
| 2.4.4.40a3.120 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 4 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 12 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$40$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + (t^2 + t)$ |
$[1, 3, 7]$ |
| 2.4.4.40a3.124 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 4 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 12 x\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$40$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t\right) x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + \left(8 t^{3} + 8 t\right) x + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + (t^2 + t)$ |
$[1, 3, 7]$ |
| 2.4.4.40a3.247 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 4 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$40$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + \left(8 t^{3} + 8\right) x + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + (t^2 + t)$ |
$[1, 3, 7]$ |
| 2.4.4.40a3.251 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 4 x + 4\right) ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4 x + 4\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$40$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, \frac{7}{2}]$ |
$[2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{2} + 4 t + 4\right) x^{3} + \left(4 t^{2} + 4 t\right) x^{2} + 8 t^{3} x + 2$ |
$[7, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + (t^2 + t)$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.44 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + \left(8 t^{2} + 8 t\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.52 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + \left(8 t^{2} + 8 t\right) x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.55 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 8 ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 4]^{4}$ |
$[1,1,1,2,3]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.56 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 8 ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 4]^{4}$ |
$[1,1,1,2,3]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 8 x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.63 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 8 ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 4]^{4}$ |
$[1,1,1,2,3]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 8 x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.64 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 8 ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 4]^{4}$ |
$[1,1,1,2,3]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 8 x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1149 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 4]^{4}$ |
$[1,1,1,2,3]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1150 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 4]^{4}$ |
$[1,1,1,2,3]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 x^{2} + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1157 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 4]^{4}$ |
$[1,1,1,2,3]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 x^{2} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1158 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 2, 3, 4]^{4}$ |
$[1,1,1,2,3]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 x^{2} + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1197 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1201 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 ( x^{4} + x + 1 )^{2} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 ) + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,2,\frac{7}{2}]$ |
$[1,1,\frac{5}{2}]$ |
$4$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 x^{2} + \left(8 t^{2} + 8 t\right) x + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.8.44d2.90 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 4 x^{6} + 2 x^{4} + 4 x^{2} + \left(8 t + 8\right) x + 4 t + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 2, 4, 16]$ |
| 2.2.8.44d2.91 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + 10 ( x^{2} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 4 x^{6} + 10 x^{4} + 4 x^{2} + \left(8 t + 8\right) x + 4 t + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 2, 4, 16]$ |
| 2.2.8.44d2.93 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 ) + 12 x + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 4 x^{6} + 10 x^{4} + 4 x^{2} + 8 x + 12 t + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 2, 4, 16]$ |
| 2.2.8.44d2.94 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + 10 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 ) + 12 x + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{7} + 4 x^{6} + 2 x^{4} + 4 x^{2} + 8 x + 12 t + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + t$ |
$[1, 2, 4, 16]$ |
| 2.2.8.48c1.358 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 x^{5} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 4 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.48c1.360 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 4\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 x^{5} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 4 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.48c1.375 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 4\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4]^{4}$ |
$[1,1,2,2,3]^{4}$ |
$[2,3]^{2}$ |
$[1,2]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 8 t x^{5} + 2 x^{4} + 8 t x^{3} + 4 x^{2} + 8 x + 4 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.48c1.376 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 4\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4]^{4}$ |
$[1,1,2,2,3]^{4}$ |
$[2,3]^{2}$ |
$[1,2]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + 2 x^{4} + 8 t x^{3} + 4 x^{2} + 8 x + 4 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.48c1.377 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 4\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4]^{4}$ |
$[1,1,2,2,3]^{4}$ |
$[2,3]^{2}$ |
$[1,2]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + 8 t x^{5} + 2 x^{4} + 8 t x^{3} + 4 x^{2} + 8 x + 4 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.48c1.381 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 4\right) ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4]^{4}$ |
$[1,1,2,2,3]^{4}$ |
$[2,3]^{2}$ |
$[1,2]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 8 t x^{3} + 4 x^{2} + 8 x + 4 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.48c1.393 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 12 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + 2 x^{4} + 8 x^{3} + 4 x^{2} + 8 x + 12 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.48c1.406 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 12 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, \frac{7}{2}, 4]^{4}$ |
$[1,1,2,\frac{5}{2},3]^{4}$ |
$[2,\frac{7}{2}]^{2}$ |
$[1,\frac{5}{2}]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 4 x^{2} + 8 x + 12 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.48c1.407 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 12 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4]^{4}$ |
$[1,1,2,2,3]^{4}$ |
$[2,3]^{2}$ |
$[1,2]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 8 t x^{3} + 4 x^{2} + 8 x + 12 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.48c1.408 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 12 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4]^{4}$ |
$[1,1,2,2,3]^{4}$ |
$[2,3]^{2}$ |
$[1,2]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 8 t x^{3} + 4 x^{2} + 8 x + 12 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.48c1.409 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 12 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4]^{4}$ |
$[1,1,2,2,3]^{4}$ |
$[2,3]^{2}$ |
$[1,2]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 8 t x^{3} + 4 x^{2} + 8 x + 12 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.48c1.413 |
$16$ |
$( x^{2} + x + 1 )^{8} + 12 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 12 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$4$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 2, 3, 3, 4]^{4}$ |
$[1,1,2,2,3]^{4}$ |
$[2,3]^{2}$ |
$[1,2]^{2}$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 4 t x^{6} + 8 t x^{5} + 2 x^{4} + 8 t x^{3} + 4 x^{2} + 8 x + 12 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.60a1.2210 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 16 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 16 t x^{6} + 4 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2214 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 16 x ( x^{2} + x + 1 )^{6} + 16 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 16 t x^{6} + 16 x^{5} + 4 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2217 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 16 x ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 16 t x^{5} + 4 x^{4} + 16 t x^{3} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2219 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(16 t + 16\right) x^{5} + 4 x^{4} + 16 t x^{3} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2238 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 16 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 16 x + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 16 t x^{5} + 4 x^{4} + 16 t x^{3} + 16 t x + 16 t + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2242 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 16 x ( x^{2} + x + 1 )^{6} + 16 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 16 x + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(16 t + 16\right) x^{5} + 4 x^{4} + 16 t x^{3} + 16 t x + 16 t + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2245 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 16 x ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 16 x + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 16 t x^{6} + 16 t x^{5} + 4 x^{4} + 16 t x + 16 t + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2247 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 16 x + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 16 t x^{6} + \left(16 t + 16\right) x^{5} + 4 x^{4} + 16 t x + 16 t + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2286 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(16 t + 8\right) x^{6} + 4 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2290 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{6} + 16 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(16 t + 8\right) x^{6} + 16 x^{5} + 4 x^{4} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2294 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{6} + 16 x ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(16 t + 8\right) x^{6} + 16 t x^{5} + 4 x^{4} + 16 t x^{3} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2296 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{6} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(16 t + 8\right) x^{6} + \left(16 t + 16\right) x^{5} + 4 x^{4} + 16 t x^{3} + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2316 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{6} + 16 x ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 16 x + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(16 t + 8\right) x^{6} + 16 x^{5} + 4 x^{4} + 16 t x^{3} + 16 t x + 16 t + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2318 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{6} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 ) + 16 x + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(16 t + 8\right) x^{6} + 4 x^{4} + 16 t x^{3} + 16 t x + 16 t + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2320 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 16 x + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(16 t + 8\right) x^{6} + 16 x^{5} + 4 x^{4} + 16 t x + 16 t + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.60a1.2324 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{6} + 16 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 x ( x^{2} + x + 1 )^{3} + 16 x ( x^{2} + x + 1 ) + 16 x + 2$ |
$2$ |
$2$ |
$8$ |
$60$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, \frac{19}{4}]$ |
$[2,3,\frac{15}{4}]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, \frac{19}{4}]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},\frac{15}{4}]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(16 t + 8\right) x^{6} + 4 x^{4} + 16 t x + 16 t + 2$ |
$[23, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.9058 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 32 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{4} + 16 x + 32 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.9062 |
$16$ |
$( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 ) + 32 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$(C_2^3\times C_4):C_4$ (as 16T292) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[2, 3, \frac{7}{2}, 4, \frac{17}{4}, 5]^{2}$ |
$[1,2,\frac{5}{2},3,\frac{13}{4},4]^{2}$ |
$[2,\frac{7}{2},\frac{17}{4}]$ |
$[1,\frac{5}{2},\frac{13}{4}]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 16 x^{7} + 4 x^{4} + 16 x + 32 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
