| 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 |
| 2.14.1.0a1.1 |
$14$ |
$x^{14} + x^{7} + x^{5} + x^{3} + 1$ |
$2$ |
$14$ |
$1$ |
$0$ |
$C_{14}$ (as 14T1) |
$14$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{14}$ |
$[\ ]^{14}$ |
$[\ ]$ |
$[\ ]$ |
$14$ |
$t^{14} + t^{7} + t^{5} + t^{3} + 1$ |
$x - 2$ |
$[0]$ |
$[\ ]$ |
|
$[1]$ |
| 2.7.2.14a1.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + 2 ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_{14}$ (as 14T1) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{7}$ |
$[1]^{7}$ |
$[\ ]$ |
$[\ ]$ |
$14$ |
$t^{7} + t + 1$ |
$x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + 1)$ |
$[1, 2]$ |
| 2.7.2.14a1.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + 2 ( x^{7} + x + 1 ) + 6$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_{14}$ (as 14T1) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{7}$ |
$[1]^{7}$ |
$[\ ]$ |
$[\ ]$ |
$14$ |
$t^{7} + t + 1$ |
$x^{2} + 2 x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + 1)$ |
$[1, 4]$ |
| 2.7.2.14a2.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + 2 x ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2 t\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.7.2.14a2.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + 2 x ( x^{7} + x + 1 ) + 6$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.7.2.14a3.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x + 2\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t^6$ |
$[1, 3]$ |
| 2.7.2.14a3.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x + 2\right) ( x^{7} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$14$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$[1,1,1,1,1,1]^{14}$ |
$[2,2,2,2,2]^{2}$ |
$[1,1,1,1,1]^{2}$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2 t + 2\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t^6$ |
$[1, 3]$ |
| 2.7.2.14a4.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + 2 x^{3} ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + 2 t^{3} x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + t^2$ |
$[1, 3]$ |
| 2.7.2.14a4.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + 2 x^{3} ( x^{7} + x + 1 ) + 6$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5}\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t^2$ |
$[1, 3]$ |
| 2.7.2.14a5.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{3} + 2\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$F_8$ (as 14T6) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{7}$ |
$[1,1,1]^{7}$ |
$[2,2]$ |
$[1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{4} + 2 t^{3} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^2 + 1)$ |
$[1, 3]$ |
| 2.7.2.14a5.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{3} + 2\right) ( x^{7} + x + 1 ) + 4 x^{6} + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2\times F_8$ (as 14T9) |
$14$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{14}$ |
$[1,1,1]^{14}$ |
$[2,2]^{2}$ |
$[1,1]^{2}$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{2} + 2\right) x + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^2 + 1)$ |
$[1, 3]$ |
| 2.7.2.14a6.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{3} + 2 x\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{7}$ |
$[1,1,1,1]^{7}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 1)$ |
$[1, 3]$ |
| 2.7.2.14a6.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{3} + 2 x\right) ( x^{7} + x + 1 ) + 6$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{7}$ |
$[1,1,1,1]^{7}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 1)$ |
$[1, 3]$ |
| 2.7.2.14a7.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{3} + 2 x + 2\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{2} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^2)$ |
$[1, 3]$ |
| 2.7.2.14a7.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{3} + 2 x + 2\right) ( x^{7} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$14$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$[1,1,1,1,1,1]^{14}$ |
$[2,2,2,2,2]^{2}$ |
$[1,1,1,1,1]^{2}$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{2} + 2\right) x + 4 t^{4} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^2)$ |
$[1, 3]$ |
| 2.7.2.14a8.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{3} + 2 x^{2}\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$14$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$[1,1,1,1,1,1]^{14}$ |
$[2,2,2,2,2]^{2}$ |
$[1,1,1,1,1]^{2}$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{3} + 2 t^{2}\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + t)$ |
$[1, 3]$ |
| 2.7.2.14a8.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{3} + 2 x^{2}\right) ( x^{7} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{4}\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + t)$ |
$[1, 3]$ |
| 2.7.2.14a9.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{3} + 2 x^{2} + 2 x + 2\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{4} + 2 t^{2} + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^2 + t)$ |
$[1, 3]$ |
| 2.7.2.14a9.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{3} + 2 x^{2} + 2 x + 2\right) ( x^{7} + x + 1 ) + 6$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{4} + 2 t^{2} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^2 + t)$ |
$[1, 3]$ |
| 2.7.2.14a10.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 2\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^3 + t^2 + t)$ |
$[1, 3]$ |
| 2.7.2.14a10.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 2\right) ( x^{7} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$14$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$[1,1,1,1,1,1]^{14}$ |
$[2,2,2,2,2]^{2}$ |
$[1,1,1,1,1]^{2}$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t^{2} + 2 t + 2\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^3 + t^2 + t)$ |
$[1, 3]$ |
| 2.7.2.14a11.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + 2 x^{5} ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{7}$ |
$[1,1,1,1]^{7}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3}\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + t^4$ |
$[1, 3]$ |
| 2.7.2.14a11.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + 2 x^{5} ( x^{7} + x + 1 ) + 6$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{7}$ |
$[1,1,1,1]^{7}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{4} + 2 t^{2}\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t^4$ |
$[1, 3]$ |
| 2.7.2.14a12.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{5} + 2 x\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$F_8$ (as 14T6) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{7}$ |
$[1,1,1]^{7}$ |
$[2,2]$ |
$[1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{4} + 2 t^{3} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.7.2.14a12.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{5} + 2 x\right) ( x^{7} + x + 1 ) + 4 x + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2\times F_8$ (as 14T9) |
$14$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{14}$ |
$[1,1,1]^{14}$ |
$[2,2]^{2}$ |
$[1,1]^{2}$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2 t\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + 1)$ |
$[1, 3]$ |
| 2.7.2.14a13.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{5} + 2 x + 2\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^4)$ |
$[1, 3]$ |
| 2.7.2.14a13.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{5} + 2 x + 2\right) ( x^{7} + x + 1 ) + 6$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2 t + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^4)$ |
$[1, 3]$ |
| 2.7.2.14a14.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{3} + 2\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{4} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^4 + t^2 + 1)$ |
$[1, 3]$ |
| 2.7.2.14a14.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{3} + 2\right) ( x^{7} + x + 1 ) + 6$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{3} + 2 t^{2} + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^4 + t^2 + 1)$ |
$[1, 3]$ |
| 2.7.2.14a15.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{4}\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t^{2} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + t^3)$ |
$[1, 3]$ |
| 2.7.2.14a15.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{4}\right) ( x^{7} + x + 1 ) + 4 x + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$14$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$[1,1,1,1,1,1]^{14}$ |
$[2,2,2,2,2]^{2}$ |
$[1,1,1,1,1]^{2}$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{3} + 2 t^{2} + 2 t\right) x + 4 t^{3} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + t^3)$ |
$[1, 3]$ |
| 2.7.2.14a16.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{3} + 2 x^{2}\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2 t^{2}\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + t^3 + t^2 + t)$ |
$[1, 3]$ |
| 2.7.2.14a16.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{5} + 2 x^{4} + 2 x^{3} + 2 x^{2}\right) ( x^{7} + x + 1 ) + 6$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{2}\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + t^3 + t^2 + t)$ |
$[1, 3]$ |
| 2.7.2.14a17.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{6} + 2 x\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + 1)$ |
$[1, 3]$ |
| 2.7.2.14a17.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{6} + 2 x\right) ( x^{7} + x + 1 ) + 4 x^{2} + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$14$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$[1,1,1,1,1,1]^{14}$ |
$[2,2,2,2,2]^{2}$ |
$[1,1,1,1,1]^{2}$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^5 + 1)$ |
$[1, 3]$ |
| 2.7.2.14a18.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{6} + 2 x + 2\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$14$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{14}$ |
$[1,1,1,1,1,1]^{14}$ |
$[2,2,2,2,2]^{2}$ |
$[1,1,1,1,1]^{2}$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t^{3} + 2\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^5)$ |
$[1, 3]$ |
| 2.7.2.14a18.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{6} + 2 x + 2\right) ( x^{7} + x + 1 ) + 4 x + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2^3:F_8$ (as 14T21) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2]$ |
$[1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{5} + 2 t^{4} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^5)$ |
$[1, 3]$ |
| 2.7.2.14a19.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{6} + 2 x^{3} + 2\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{4} + 2 t^{2} + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + t^2 + 1)$ |
$[1, 3]$ |
| 2.7.2.14a19.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(2 x^{6} + 2 x^{3} + 2\right) ( x^{7} + x + 1 ) + 6$ |
$2$ |
$7$ |
$2$ |
$14$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2, 2, 2]^{7}$ |
$[1,1,1,1,1,1,1]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(2 t^{6} + 2 t^{5} + 2 t^{4} + 2 t^{2} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + t^2 + 1)$ |
$[1, 3]$ |
| 2.7.2.21a1.1 |
$14$ |
$( x^{7} + x + 1 )^{2} + 2$ |
$2$ |
$7$ |
$2$ |
$21$ |
$C_{14}$ (as 14T1) |
$7$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{7}$ |
$[2]^{7}$ |
$[\ ]$ |
$[\ ]$ |
$14$ |
$t^{7} + t + 1$ |
$x^{2} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + 1)$ |
$[1, 3]$ |
| 2.7.2.21a1.2 |
$14$ |
$( x^{7} + x + 1 )^{2} + 10$ |
$2$ |
$7$ |
$2$ |
$21$ |
$C_{14}$ (as 14T1) |
$7$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{7}$ |
$[2]^{7}$ |
$[\ ]$ |
$[\ ]$ |
$14$ |
$t^{7} + t + 1$ |
$x^{2} + 10$ |
$[2, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + 1)$ |
$[1, 3]$ |
| 2.7.2.21a1.3 |
$14$ |
$( x^{7} + x + 1 )^{2} + 4 x^{3} ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$[1,1,1,1,1,1,2]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{5}\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + 1)$ |
$[1, 3]$ |
| 2.7.2.21a1.4 |
$14$ |
$( x^{7} + x + 1 )^{2} + 4 x^{3} ( x^{7} + x + 1 ) + 10$ |
$2$ |
$7$ |
$2$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$[1,1,1,1,1,1,2]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + 4 t^{6} x + 10$ |
$[2, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + 1)$ |
$[1, 3]$ |
| 2.7.2.21a1.5 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(4 x^{4} + 4 x^{3}\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$[1,1,1,1,1,1,2]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + 4 t^{5} x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + 1)$ |
$[1, 3]$ |
| 2.7.2.21a1.6 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(4 x^{4} + 4 x^{3}\right) ( x^{7} + x + 1 ) + 10$ |
$2$ |
$7$ |
$2$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$[1,1,1,1,1,1,2]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{2} + 4 t\right) x + 10$ |
$[2, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + 1)$ |
$[1, 3]$ |
| 2.7.2.21a1.7 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(4 x^{3} + 4 x^{2}\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$[1,1,1,1,1,1,2]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{5} + 4 t^{3} + 4 t^{2}\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + 1)$ |
$[1, 3]$ |
| 2.7.2.21a1.8 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(4 x^{3} + 4 x^{2}\right) ( x^{7} + x + 1 ) + 10$ |
$2$ |
$7$ |
$2$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$[1,1,1,1,1,1,2]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{6} + 4 t^{5} + 4 t^{3} + 4 t^{2}\right) x + 10$ |
$[2, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + 1)$ |
$[1, 3]$ |
| 2.7.2.21a1.9 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(4 x^{4} + 4 x^{3} + 4 x^{2}\right) ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$[1,1,1,1,1,1,2]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + 1)$ |
$[1, 3]$ |
| 2.7.2.21a1.10 |
$14$ |
$( x^{7} + x + 1 )^{2} + \left(4 x^{4} + 4 x^{3} + 4 x^{2}\right) ( x^{7} + x + 1 ) + 10$ |
$2$ |
$7$ |
$2$ |
$21$ |
$C_2 \wr C_7$ (as 14T29) |
$7$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 2, 2, 3]^{7}$ |
$[1,1,1,1,1,1,2]^{7}$ |
$[2,2,2,2,2,2]$ |
$[1,1,1,1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + \left(4 t^{5} + 4 t^{4} + 4 t^{3} + 4 t\right) x + 10$ |
$[2, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + 1)$ |
$[1, 3]$ |
| 2.7.2.21a1.11 |
$14$ |
$( x^{7} + x + 1 )^{2} + 4 x ( x^{7} + x + 1 ) + 2$ |
$2$ |
$7$ |
$2$ |
$21$ |
$C_2\times F_8$ (as 14T9) |
$7$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 3]^{7}$ |
$[1,1,1,2]^{7}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{7} + t + 1$ |
$x^{2} + 4 t^{4} x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + (t^6 + t^5 + 1)$ |
$[1, 3]$ |
