| 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 |
| 2.4.4.24a1.3 |
$16$ |
$( x^{4} + x + 1 )^{4} + 2 ( x^{4} + x + 1 )^{3} + 4 x + 2$ |
$2$ |
$4$ |
$4$ |
$24$ |
$C_8: C_2$ (as 16T6) |
$4$ |
$1$ |
$[2, 2]$ |
$[1,1]$ |
$[2, 2]^{4}$ |
$[1,1]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{4} + t + 1$ |
$x^{4} + 2 x^{3} + 4 t + 2$ |
$[3, 3, 0]$ |
$[1]$ |
$z^3 + 1$ |
$[1, 3, 6]$ |
| 2.4.4.32b1.9 |
$16$ |
$( x^{4} + x + 1 )^{4} + 4 ( x^{4} + x + 1 )^{3} + 2 ( x^{4} + x + 1 )^{2} + 4 ( x^{4} + x + 1 ) + 8 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$32$ |
$C_8: C_2$ (as 16T6) |
$4$ |
$1$ |
$[2, 3]$ |
$[1,2]$ |
$[2, 3]^{4}$ |
$[1,2]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{4} + t + 1$ |
$x^{4} + 4 x^{3} + 2 x^{2} + 4 x + 8 t^{3} + 2$ |
$[5, 2, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 7, 11]$ |
| 2.4.4.44a1.54 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_8: C_2$ (as 16T6) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{4}$ |
$[2,3]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.4.4.44a1.62 |
$16$ |
$( x^{4} + x + 1 )^{4} + 8 ( x^{4} + x + 1 )^{3} + 8 ( x^{4} + x + 1 ) + 16 x^{3} + 2$ |
$2$ |
$4$ |
$4$ |
$44$ |
$C_8: C_2$ (as 16T6) |
$4$ |
$1$ |
$[3, 4]$ |
$[2,3]$ |
$[3, 4]^{4}$ |
$[2,3]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{4} + t + 1$ |
$x^{4} + 8 x^{3} + 8 x + 16 t^{3} + 2$ |
$[8, 4, 0]$ |
$[1, 1]$ |
$z^2 + 1,z + 1$ |
$[1, 3, 7]$ |
| 2.2.8.40d1.33 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 12 x + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[2, 3, 3]$ |
$[1,2,2]$ |
$[2, 3, 3]^{2}$ |
$[1,2,2]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 4 x^{5} + 2 x^{4} + 12 t + 2$ |
$[13, 12, 4, 0]$ |
$[1, 1]$ |
$z^4 + 1,z^3 + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.40d1.34 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 x ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 12 x + 10$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[2, 3, 3]$ |
$[1,2,2]$ |
$[2, 3, 3]^{2}$ |
$[1,2,2]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 4 t x^{6} + 4 x^{5} + 2 x^{4} + 12 t + 10$ |
$[13, 12, 4, 0]$ |
$[1, 1]$ |
$z^4 + 1,z^3 + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.40d1.43 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 4 x + 2$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[2, 3, 3]$ |
$[1,2,2]$ |
$[2, 3, 3]^{2}$ |
$[1,2,2]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + \left(4 t + 4\right) x^{6} + 4 x^{5} + 2 x^{4} + 4 t + 2$ |
$[13, 12, 4, 0]$ |
$[1, 1]$ |
$z^4 + 1,z^3 + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.40d1.45 |
$16$ |
$( x^{2} + x + 1 )^{8} + 4 ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 4 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 4 ( x^{2} + x + 1 ) + 4 x + 10$ |
$2$ |
$2$ |
$8$ |
$40$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[2, 3, 3]$ |
$[1,2,2]$ |
$[2, 3, 3]^{2}$ |
$[1,2,2]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 4 x^{7} + \left(4 t + 4\right) x^{6} + 4 x^{5} + 2 x^{4} + 4 t + 10$ |
$[13, 12, 4, 0]$ |
$[1, 1]$ |
$z^4 + 1,z^3 + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.48c1.45 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 8 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 2 x^{4} + 4 x^{2} + 8 x + 8 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 16, 24]$ |
| 2.2.8.48c1.46 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 8\right) ( x^{2} + x + 1 )^{7} + 8 ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 4 ( x^{2} + x + 1 )^{2} + 24 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 2 x^{4} + 4 x^{2} + 8 x + 24 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 16, 24]$ |
| 2.2.8.48c1.399 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 12 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 2 x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + 8 x + 12 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.48c1.400 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(8 x + 12\right) ( x^{2} + x + 1 )^{7} + \left(4 x + 4\right) ( x^{2} + x + 1 )^{6} + 8 x ( x^{2} + x + 1 )^{5} + 2 ( x^{2} + x + 1 )^{4} + 8 x ( x^{2} + x + 1 )^{3} + \left(8 x + 12\right) ( x^{2} + x + 1 ) + 28 x + 2$ |
$2$ |
$2$ |
$8$ |
$48$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[2, 3, 4]$ |
$[1,2,3]$ |
$[2, 3, 4]^{2}$ |
$[1,2,3]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 8 t x^{7} + 4 t x^{6} + 2 x^{4} + \left(8 t + 8\right) x^{3} + 4 x^{2} + 8 x + 28 t + 2$ |
$[17, 10, 4, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 16]$ |
| 2.2.8.62a1.9019 |
$16$ |
$( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.9020 |
$16$ |
$( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 32 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 32 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.9023 |
$16$ |
$( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 16 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.9024 |
$16$ |
$( x^{2} + x + 1 )^{8} + 16 ( x^{2} + x + 1 )^{7} + 16 ( x^{2} + x + 1 )^{5} + 4 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 32 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 16 x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 32 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.9129 |
$16$ |
$( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 16 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + \left(16 t + 16\right) x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 16 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.9130 |
$16$ |
$( x^{2} + x + 1 )^{8} + 16 x ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 48 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + \left(16 t + 16\right) x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 48 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.9131 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 16 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 16 t x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 16 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.2.8.62a1.9132 |
$16$ |
$( x^{2} + x + 1 )^{8} + \left(16 x + 16\right) ( x^{2} + x + 1 )^{7} + 4 ( x^{2} + x + 1 )^{4} + 16 ( x^{2} + x + 1 )^{3} + 16 ( x^{2} + x + 1 ) + 48 x + 2$ |
$2$ |
$2$ |
$8$ |
$62$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$1$ |
$[3, 4, 5]$ |
$[2,3,4]$ |
$[3, 4, 5]^{2}$ |
$[2,3,4]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + t + 1$ |
$x^{8} + 16 t x^{7} + 16 x^{5} + 4 x^{4} + 16 x^{3} + 48 t + 2$ |
$[24, 16, 8, 0]$ |
$[1, 1, 1]$ |
$z^4 + 1,z^2 + 1,z + 1$ |
$[1, 3, 7, 15]$ |
| 2.1.16.64g1.1 |
$16$ |
$x^{16} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 2$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 27, 43, 59, 75]$ |
| 2.1.16.64g1.2 |
$16$ |
$x^{16} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 34$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 34$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 27, 43, 59, 75]$ |
| 2.1.16.64g1.50 |
$16$ |
$x^{16} + 16 x^{15} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 18$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 16 x^{15} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 18$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 32, 48, 64]$ |
| 2.1.16.64g1.51 |
$16$ |
$x^{16} + 16 x^{15} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 50$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 16 x^{15} + 2 x^{8} + 4 x^{4} + 8 x^{2} + 16 x + 50$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 32, 48, 64]$ |
| 2.1.16.64g1.756 |
$16$ |
$x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 4 x^{4} + 8 x^{2} + 16 x + 10$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 4 x^{4} + 8 x^{2} + 16 x + 10$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 32, 48]$ |
| 2.1.16.64g1.757 |
$16$ |
$x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 4 x^{4} + 8 x^{2} + 16 x + 42$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 4 x^{4} + 8 x^{2} + 16 x + 42$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 32, 48]$ |
| 2.1.16.64g1.805 |
$16$ |
$x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 4 x^{4} + 8 x^{2} + 16 x + 26$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 4 x^{4} + 8 x^{2} + 16 x + 26$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 32, 48]$ |
| 2.1.16.64g1.806 |
$16$ |
$x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 4 x^{4} + 8 x^{2} + 16 x + 58$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 16 x^{15} + 8 x^{14} + 16 x^{13} + 16 x^{11} + 2 x^{8} + 16 x^{7} + 4 x^{4} + 8 x^{2} + 16 x + 58$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 32, 48]$ |
| 2.1.16.64g1.3997 |
$16$ |
$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 6$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 6$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.64g1.3998 |
$16$ |
$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 38$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 38$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.64g1.4046 |
$16$ |
$x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 22$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 22$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.64g1.4047 |
$16$ |
$x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 54$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 16 x^{15} + 16 x^{13} + 4 x^{12} + 16 x^{9} + 2 x^{8} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 54$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.64g1.4740 |
$16$ |
$x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 14$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.64g1.4741 |
$16$ |
$x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 46$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 8 x^{14} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 46$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.64g1.4789 |
$16$ |
$x^{16} + 16 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 16 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 30$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 2.1.16.64g1.4790 |
$16$ |
$x^{16} + 16 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 62$ |
$2$ |
$1$ |
$16$ |
$64$ |
$C_8: C_2$ (as 16T6) |
$1$ |
$1$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[2, 3, 4, 5]$ |
$[1,2,3,4]$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t + 1$ |
$x^{16} + 16 x^{15} + 8 x^{14} + 4 x^{12} + 16 x^{11} + 16 x^{9} + 2 x^{8} + 16 x^{7} + 8 x^{6} + 4 x^{4} + 16 x^{3} + 8 x^{2} + 16 x + 62$ |
$[49, 34, 20, 8, 0]$ |
$[1, 1, 1, 1]$ |
$z^8 + 1,z^4 + 1,z^2 + 1,z + 1$ |
$[1, 2, 4, 8, 32]$ |
| 3.4.4.12a1.1 |
$16$ |
$( x^{4} + 2 x^{3} + 2 )^{4} + 3 x^{2}$ |
$3$ |
$4$ |
$4$ |
$12$ |
$C_8: C_2$ (as 16T6) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$[\ ]_{4}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{4} + 3 t^{2}$ |
$[0]$ |
$[1]$ |
$z^3 + z^2 + 1$ |
$[2]$ |
| 5.2.8.14a1.3 |
$16$ |
$( x^{2} + 4 x + 2 )^{8} + 5$ |
$5$ |
$2$ |
$8$ |
$14$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + 4 t + 2$ |
$x^{8} + 5$ |
$[0]$ |
$[1]$ |
$z^7 + 3 z^6 + 3 z^5 + z^4 + z^2 + 3 z + 3$ |
$[2]$ |
| 5.2.8.14a1.4 |
$16$ |
$( x^{2} + 4 x + 2 )^{8} + 10$ |
$5$ |
$2$ |
$8$ |
$14$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + 4 t + 2$ |
$x^{8} + 10$ |
$[0]$ |
$[1]$ |
$z^7 + 3 z^6 + 3 z^5 + z^4 + z^2 + 3 z + 3$ |
undefined |
| 5.2.8.14a1.5 |
$16$ |
$( x^{2} + 4 x + 2 )^{8} + 10 x + 10$ |
$5$ |
$2$ |
$8$ |
$14$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + 4 t + 2$ |
$x^{8} + 10 t + 10$ |
$[0]$ |
$[1]$ |
$z^7 + 3 z^6 + 3 z^5 + z^4 + z^2 + 3 z + 3$ |
$[2]$ |
| 5.2.8.14a1.6 |
$16$ |
$( x^{2} + 4 x + 2 )^{8} + 5 x + 15$ |
$5$ |
$2$ |
$8$ |
$14$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + 4 t + 2$ |
$x^{8} + 5 t + 15$ |
$[0]$ |
$[1]$ |
$z^7 + 3 z^6 + 3 z^5 + z^4 + z^2 + 3 z + 3$ |
undefined |
| 7.4.4.12a1.1 |
$16$ |
$( x^{4} + 5 x^{2} + 4 x + 3 )^{4} + 7 x^{2}$ |
$7$ |
$4$ |
$4$ |
$12$ |
$C_8: C_2$ (as 16T6) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$[\ ]_{4}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{4} + 5 t^{2} + 4 t + 3$ |
$x^{4} + 7 t^{2}$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 11.4.4.12a1.1 |
$16$ |
$( x^{4} + 8 x^{2} + 10 x + 2 )^{4} + 11 x^{2}$ |
$11$ |
$4$ |
$4$ |
$12$ |
$C_8: C_2$ (as 16T6) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$[\ ]_{4}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{4} + 8 t^{2} + 10 t + 2$ |
$x^{4} + 11 t^{2}$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 13.2.8.14a1.2 |
$16$ |
$( x^{2} + 12 x + 2 )^{8} + 13$ |
$13$ |
$2$ |
$8$ |
$14$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + 12 t + 2$ |
$x^{8} + 13$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 2 z^5 + 4 z^4 + 5 z^3 + 4 z^2 + 2 z + 8$ |
undefined |
| 13.2.8.14a1.3 |
$16$ |
$( x^{2} + 12 x + 2 )^{8} + 65 x + 26$ |
$13$ |
$2$ |
$8$ |
$14$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + 12 t + 2$ |
$x^{8} + 65 t + 26$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 2 z^5 + 4 z^4 + 5 z^3 + 4 z^2 + 2 z + 8$ |
undefined |
| 13.2.8.14a1.4 |
$16$ |
$( x^{2} + 12 x + 2 )^{8} + 130 x + 26$ |
$13$ |
$2$ |
$8$ |
$14$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + 12 t + 2$ |
$x^{8} + 130 t + 26$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 2 z^5 + 4 z^4 + 5 z^3 + 4 z^2 + 2 z + 8$ |
undefined |
| 13.2.8.14a1.6 |
$16$ |
$( x^{2} + 12 x + 2 )^{8} + 13 x + 143$ |
$13$ |
$2$ |
$8$ |
$14$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + 12 t + 2$ |
$x^{8} + 13 t + 143$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 2 z^5 + 4 z^4 + 5 z^3 + 4 z^2 + 2 z + 8$ |
undefined |
| 19.4.4.12a1.1 |
$16$ |
$( x^{4} + 2 x^{2} + 11 x + 2 )^{4} + 19 x^{2}$ |
$19$ |
$4$ |
$4$ |
$12$ |
$C_8: C_2$ (as 16T6) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$[\ ]_{4}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{4} + 2 t^{2} + 11 t + 2$ |
$x^{4} + 19 t^{2}$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 23.4.4.12a1.1 |
$16$ |
$( x^{4} + 3 x^{2} + 19 x + 5 )^{4} + 23 x^{2}$ |
$23$ |
$4$ |
$4$ |
$12$ |
$C_8: C_2$ (as 16T6) |
$4$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{4}$ |
$[\ ]_{4}^{4}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{4} + 3 t^{2} + 19 t + 5$ |
$x^{4} + 23 t^{2}$ |
$[0]$ |
$[1]$ |
$z^3 + 4 z^2 + 6 z + 4$ |
undefined |
| 29.2.8.14a1.2 |
$16$ |
$( x^{2} + 24 x + 2 )^{8} + 29$ |
$29$ |
$2$ |
$8$ |
$14$ |
$C_8: C_2$ (as 16T6) |
$2$ |
$8$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{8}^{2}$ |
$[\ ]_{8}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$16$ |
$t^{2} + 24 t + 2$ |
$x^{8} + 29$ |
$[0]$ |
$[1]$ |
$z^7 + 8 z^6 + 28 z^5 + 27 z^4 + 12 z^3 + 27 z^2 + 28 z + 8$ |
undefined |
