| 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 |
| 2.2.8.54a1.380 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 8 x^{5} + \left(8 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.515 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 8 x^{5} + \left(8 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.520 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(8 t + 8\right) x^{7} + 8 x^{5} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.759 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.763 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 24 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 8 t x^{5} + \left(24 t + 2\right) x^{4} + \left(16 t + 16\right) x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.864 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 2\right) x^{4} + 8 t x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.866 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + 4 x ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + \left(24 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + \left(8 t + 8\right) x^{5} + \left(16 t + 2\right) x^{4} + 16 t x^{3} + 8 t x^{2} + 16 t x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1381 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 8 x^{5} + \left(8 t + 2\right) x^{4} + 16 x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1417 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1419 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 16 t x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1421 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1423 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 16 ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 x^{5} + 2 x^{4} + 16 t x^{3} + 8 t x^{2} + 16 x + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1872 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + \left(16 t + 2\right) x^{4} + 16 t x^{3} + \left(8 t + 8\right) x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.1875 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, 4, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},3,\frac{7}{2}]^{2}$ |
$[2,3,4]$ |
$[1,2,3]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{6} + 8 t x^{5} + 2 x^{4} + \left(8 t + 8\right) x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.2224 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 8\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 16 x^{3} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
| 2.2.8.54a1.2228 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{5} + \left(16 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(16 x + 24\right) ( x^{2} + x + 1 )^{3} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$54$ |
$C_4^2.D_4$ (as 16T343) |
$2$ |
$1$ |
$[2, \frac{7}{2}, \frac{9}{2}]$ |
$[1,\frac{5}{2},\frac{7}{2}]$ |
$[2, 2, 3, \frac{7}{2}, \frac{7}{2}, \frac{9}{2}]^{2}$ |
$[1,1,2,\frac{5}{2},\frac{5}{2},\frac{7}{2}]^{2}$ |
$[2,3,\frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$2$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + \left(4 t + 4\right) x^{6} + \left(8 t + 8\right) x^{5} + 2 x^{4} + 8 t x^{2} + 2$ |
$[20, 12, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 5, 13, 21]$ |
