| 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 |
| 2.2.8.44d5.7 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 3, 3, \frac{7}{2}]^{2}$ |
$[1,2,2,\frac{5}{2}]^{2}$ |
$[3]$ |
$[2]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + \left(4 t + 4\right) x^{6} + 2 x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 8 t x + 10$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 5, 13, 21]$ |
| 2.2.8.44d5.19 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{7} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 3, 3, \frac{7}{2}]^{2}$ |
$[1,2,2,\frac{5}{2}]^{2}$ |
$[3]$ |
$[2]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + \left(4 t + 4\right) x^{6} + 2 x^{4} + \left(8 t + 8\right) x^{3} + 4 t x^{2} + 8 t x + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 5, 13, 21]$ |
| 2.2.8.44d5.76 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 2$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 3, 3, \frac{7}{2}]^{2}$ |
$[1,2,2,\frac{5}{2}]^{2}$ |
$[3]$ |
$[2]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + \left(8 t + 2\right) x^{4} + 8 x^{3} + 4 t x^{2} + 8 t x + 2$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 5, 13, 21]$ |
| 2.2.8.44d5.88 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + \left(8 x + 2\right) ( x^{2} + x + 1 )^{4} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{3} + 4 x ( x^{2} + x + 1 )^{2} + 8 x ( x^{2} + x + 1 ) + 10$ |
$2$ |
$2$ |
$8$ |
$44$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}]$ |
$[1,2,\frac{5}{2}]$ |
$[2, 3, 3, \frac{7}{2}]^{2}$ |
$[1,2,2,\frac{5}{2}]^{2}$ |
$[3]$ |
$[2]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + \left(4 t + 4\right) x^{7} + \left(8 t + 2\right) x^{4} + 8 x^{3} + 4 t x^{2} + 8 t x + 10$ |
$[15, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + t,t z + (t + 1)$ |
$[1, 5, 13, 21]$ |
| 2.2.8.52c1.15 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 x + 2$ |
$2$ |
$2$ |
$8$ |
$52$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[3, \frac{7}{2}, 4]$ |
$[2,\frac{5}{2},3]$ |
$[2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 t x^{4} + 8 x^{3} + 8 x^{2} + 16 t + 2$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.52c1.34 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 8 x ( x^{2} + x + 1 )^{2} + 2$ |
$2$ |
$2$ |
$8$ |
$52$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[3, \frac{7}{2}, 4]$ |
$[2,\frac{5}{2},3]$ |
$[2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 x^{6} + 8 t x^{5} + 8 x^{3} + 8 t x^{2} + 2$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.52c1.246 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 ( x^{2} + x + 1 )^{3} + 8 ( x^{2} + x + 1 )^{2} + 16 x + 2$ |
$2$ |
$2$ |
$8$ |
$52$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[3, \frac{7}{2}, 4]$ |
$[2,\frac{5}{2},3]$ |
$[2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + 8 x^{5} + \left(8 t + 4\right) x^{4} + 8 x^{3} + 8 x^{2} + 16 t + 2$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.52c1.272 |
$16$ |
$( x^{2} + x + 1 )^{8} + 8 ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + \left(8 x + 4\right) ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{2} + 16 x + 2$ |
$2$ |
$2$ |
$8$ |
$52$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[3, \frac{7}{2}, 4]$ |
$[2,\frac{5}{2},3]$ |
$[2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[2]$ |
$[1]$ |
$4$ |
$t^{2} + t + 1$ |
$x^{8} + 8 x^{7} + 4 x^{6} + \left(8 t + 8\right) x^{5} + \left(8 t + 4\right) x^{4} + 8 x^{3} + 8 t x^{2} + 16 t + 2$ |
$[19, 14, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.16.52k1.4 |
$16$ |
$x^{16} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 18$ |
$2$ |
$1$ |
$16$ |
$52$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, 3, 4]$ |
$[1,2,2,3]$ |
$[2, 3, 3, 4]^{2}$ |
$[1,2,2,3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 18$ |
$[37, 26, 24, 8, 0]$ |
$[1, 2, 1]$ |
$z^8 + 1,z^6 + 1,z + 1$ |
$[1, 5, 25, 41, 57]$ |
| 2.1.16.52k1.28 |
$16$ |
$x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 26$ |
$2$ |
$1$ |
$16$ |
$52$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, 3, 4]$ |
$[1,2,2,3]$ |
$[2, 3, 3, 4]^{2}$ |
$[1,2,2,3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 8 x^{15} + 8 x^{13} + 8 x^{11} + 4 x^{10} + 2 x^{8} + 8 x^{5} + 26$ |
$[37, 26, 24, 8, 0]$ |
$[1, 2, 1]$ |
$z^8 + 1,z^6 + 1,z + 1$ |
$[1, 5, 10, 32, 48]$ |
| 2.1.16.52k1.136 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 18$ |
$2$ |
$1$ |
$16$ |
$52$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, 3, 4]$ |
$[1,2,2,3]$ |
$[2, 3, 3, 4]^{2}$ |
$[1,2,2,3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 18$ |
$[37, 26, 24, 8, 0]$ |
$[1, 2, 1]$ |
$z^8 + 1,z^6 + 1,z + 1$ |
$[1, 5, 25, 41, 57]$ |
| 2.1.16.52k1.144 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 18$ |
$2$ |
$1$ |
$16$ |
$52$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, 3, 4]$ |
$[1,2,2,3]$ |
$[2, 3, 3, 4]^{2}$ |
$[1,2,2,3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 18$ |
$[37, 26, 24, 8, 0]$ |
$[1, 2, 1]$ |
$z^8 + 1,z^6 + 1,z + 1$ |
$[1, 5, 31, 47, 63]$ |
| 2.1.16.52k1.160 |
$16$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 26$ |
$2$ |
$1$ |
$16$ |
$52$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, 3, 4]$ |
$[1,2,2,3]$ |
$[2, 3, 3, 4]^{2}$ |
$[1,2,2,3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 4 x^{10} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 26$ |
$[37, 26, 24, 8, 0]$ |
$[1, 2, 1]$ |
$z^8 + 1,z^6 + 1,z + 1$ |
$[1, 5, 10, 32, 48]$ |
| 2.1.16.52k1.168 |
$16$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 26$ |
$2$ |
$1$ |
$16$ |
$52$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, 3, 4]$ |
$[1,2,2,3]$ |
$[2, 3, 3, 4]^{2}$ |
$[1,2,2,3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{11} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 26$ |
$[37, 26, 24, 8, 0]$ |
$[1, 2, 1]$ |
$z^8 + 1,z^6 + 1,z + 1$ |
$[1, 5, 10, 32, 48]$ |
| 2.1.16.52k1.228 |
$16$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 22$ |
$2$ |
$1$ |
$16$ |
$52$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, 3, 4]$ |
$[1,2,2,3]$ |
$[2, 3, 3, 4]^{2}$ |
$[1,2,2,3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 22$ |
$[37, 26, 24, 8, 0]$ |
$[1, 2, 1]$ |
$z^8 + 1,z^6 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.52k1.248 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 30$ |
$2$ |
$1$ |
$16$ |
$52$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, 3, 4]$ |
$[1,2,2,3]$ |
$[2, 3, 3, 4]^{2}$ |
$[1,2,2,3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{10} + 8 x^{9} + 2 x^{8} + 8 x^{7} + 8 x^{5} + 30$ |
$[37, 26, 24, 8, 0]$ |
$[1, 2, 1]$ |
$z^8 + 1,z^6 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.54o1.103 |
$16$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 18$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 18$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 7, 31, 47, 63]$ |
| 2.1.16.54o1.165 |
$16$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 26$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 8 x^{13} + 4 x^{12} + 8 x^{9} + 10 x^{8} + 8 x^{7} + 4 x^{4} + 26$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 7, 14, 32, 48]$ |
| 2.1.16.54o1.266 |
$16$ |
$x^{16} + 4 x^{14} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 22$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 4 x^{14} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 22$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.54o1.325 |
$16$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 30$ |
$2$ |
$1$ |
$16$ |
$54$ |
$C_4^2:C_2$ (as 16T27) |
$2$ |
$1$ |
$[2, 3, \frac{7}{2}, 4]$ |
$[1,2,\frac{5}{2},3]$ |
$[2, 3, \frac{7}{2}, 4]^{2}$ |
$[1,2,\frac{5}{2},3]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$4$ |
$t + 1$ |
$x^{16} + 8 x^{15} + 4 x^{14} + 10 x^{8} + 8 x^{7} + 8 x^{6} + 4 x^{4} + 8 x^{2} + 30$ |
$[39, 30, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
