| 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 |
| 2.4.4.36a5.353 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2} + 4\right) x^{3} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.354 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2} + 4\right) x^{3} + \left(2 t^{3} + 2\right) x^{2} + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.357 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{3} + 2\right) x^{2} + \left(8 t + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.358 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + \left(8 t + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.361 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2} + 4\right) x^{3} + \left(2 t^{3} + 2\right) x^{2} + 8 x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.362 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2} + 4\right) x^{3} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + 8 x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.365 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + \left(8 x + 8\right) ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + 8 t x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.366 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + \left(8 x + 8\right) ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{3} + 2\right) x^{2} + 8 t x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.369 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{3} + 2\right) x^{2} + 8 t^{3} x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.370 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + 8 t^{3} x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.373 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2} + 4\right) x^{3} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.374 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2} + 4\right) x^{3} + \left(2 t^{3} + 2\right) x^{2} + \left(8 t^{3} + 8 t + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.377 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + \left(8 t^{3} + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.378 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 x^{3} + \left(2 t^{3} + 2\right) x^{2} + \left(8 t^{3} + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.381 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + \left(8 x + 8\right) ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2} + 4\right) x^{3} + \left(2 t^{3} + 2\right) x^{2} + \left(8 t^{3} + 8 t\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.382 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 2\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + \left(8 x + 8\right) ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2} + 4\right) x^{3} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + \left(8 t^{3} + 8 t\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.483 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(2 t^{3} + 2\right) x^{2} + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.484 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.487 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + 8 t^{2} x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.488 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(2 t^{3} + 2\right) x^{2} + 8 t^{2} x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.491 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + 8 x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.492 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(2 t^{3} + 2\right) x^{2} + 8 x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.495 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(2 t^{3} + 2\right) x^{2} + \left(8 t^{2} + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.496 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + \left(8 t^{2} + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.497 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2}\right) x^{3} + \left(2 t^{3} + 2\right) x^{2} + 8 t^{2} x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.498 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2}\right) x^{3} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + 8 t^{2} x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.501 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2}\right) x^{3} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.502 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + 8 x ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2}\right) x^{3} + \left(2 t^{3} + 2\right) x^{2} + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.505 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2}\right) x^{3} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + \left(8 t^{2} + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.506 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + 8 ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2}\right) x^{3} + \left(2 t^{3} + 2\right) x^{2} + \left(8 t^{2} + 8\right) x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.509 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 2 x + 2\right) ( x^{4} + x + 1 )^{2} + \left(8 x + 8\right) ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2}\right) x^{3} + \left(2 t^{3} + 2\right) x^{2} + 8 x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.36a5.510 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{3} + 6 x^{2} + 4 x + 6\right) ( x^{4} + x + 1 )^{3} + \left(2 x^{3} + 10 x + 2\right) ( x^{4} + x + 1 )^{2} + \left(8 x + 8\right) ( x^{4} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$4$ |
$4$ |
$36$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$4$ |
$1$ |
$[2, \frac{7}{2}]$ |
$[1,\frac{5}{2}]$ |
$[2, 2, 2, 3, 3, \frac{7}{2}, \frac{7}{2}, \frac{7}{2}]^{4}$ |
$[1,1,1,2,2,\frac{5}{2},\frac{5}{2},\frac{5}{2}]^{4}$ |
$[2,2,3,3,\frac{7}{2},\frac{7}{2}]$ |
$[1,1,2,2,\frac{5}{2},\frac{5}{2}]$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(4 t^{3} + 4 t^{2}\right) x^{3} + \left(2 t^{3} + 8 t^{2} + 2\right) x^{2} + 8 x + 4 t + 2$ |
$[6, 2, 0]$ |
$[1, 1]$ |
$z^2 + (t^3 + t + 1),(t^3 + t + 1) z + (t^3 + t + 1)$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.423 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.424 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.425 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{2} ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.426 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2}\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8\right) x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.427 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.428 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t\right) x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.429 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t\right) x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.430 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2}\right) x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.431 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.432 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t\right) x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.433 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.434 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.435 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8\right) x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.436 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.437 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{2} + 8 t + 8\right) x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.438 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(8 x^{3} + 8 x^{2} + 8 x + 8\right) ( x^{4} + x + 1 )^{3} + 4 x^{2} ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + \left(8 t^{3} + 8 t^{2} + 8\right) x^{3} + 4 t x^{2} + 8 t x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1531 |
$16$ |
$( x^{4} + x + 1 )^{4} + \left(4 x^{2} + 4\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{2} x^{3} + 4 t x^{2} + \left(8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.1532 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 x^{3} ( x^{4} + x + 1 )^{3} + \left(4 x^{2} + 4\right) ( x^{4} + x + 1 )^{2} + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$(C_2^2\times C_4^2).\OD_{16}$ (as 16T1243) |
$8$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[2, 2, 3, 3, 3, \frac{7}{2}, 4]^{8}$ |
$[1,1,2,2,2,\frac{5}{2},3]^{8}$ |
$[2,2,3,3,\frac{7}{2}]_{2}$ |
$[1,1,2,2,\frac{5}{2}]_{2}$ |
$2$ |
$t^{4} + t + 1$ |
$x^{4} + 8 t^{3} x^{3} + 4 t x^{2} + \left(8 t + 8\right) x + 8 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
