| 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 |
| 2.10.1.0a1.1 |
$10$ |
$x^{10} + x^{6} + x^{5} + x^{3} + x^{2} + x + 1$ |
$2$ |
$10$ |
$1$ |
$0$ |
$C_{10}$ (as 10T1) |
$10$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{10}$ |
$[\ ]^{10}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{10} + t^{6} + t^{5} + t^{3} + t^{2} + t + 1$ |
$x - 2$ |
$[0]$ |
$[\ ]$ |
|
$[1]$ |
| 2.5.2.10a1.1 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + 2 ( x^{5} + x^{2} + 1 ) + 2$ |
$2$ |
$5$ |
$2$ |
$10$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{5}$ |
$[1]^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 2]$ |
| 2.5.2.10a1.2 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + 2 ( x^{5} + x^{2} + 1 ) + 6$ |
$2$ |
$5$ |
$2$ |
$10$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{5}$ |
$[1]^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 2 x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 4]$ |
| 2.5.2.10a2.1 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + 2 x ( x^{5} + x^{2} + 1 ) + 2$ |
$2$ |
$5$ |
$2$ |
$10$ |
$C_2^4 : C_5$ (as 10T8) |
$5$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{5}$ |
$[1,1,1,1]^{5}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t$ |
$[1, 3]$ |
| 2.5.2.10a2.2 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + 2 x ( x^{5} + x^{2} + 1 ) + 4 x^{2} + 2$ |
$2$ |
$5$ |
$2$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$10$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{10}$ |
$[1,1,1,1]^{10}$ |
$[2,2,2]^{2}$ |
$[1,1,1]^{2}$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 2 t x + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t$ |
$[1, 3]$ |
| 2.5.2.10a3.1 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(2 x^{2} + 2\right) ( x^{5} + x^{2} + 1 ) + 2$ |
$2$ |
$5$ |
$2$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$[1,1,1,1,1]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 1)$ |
$[1, 3]$ |
| 2.5.2.10a3.2 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(2 x^{2} + 2\right) ( x^{5} + x^{2} + 1 ) + 6$ |
$2$ |
$5$ |
$2$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$[1,1,1,1,1]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 1)$ |
$[1, 3]$ |
| 2.5.2.10a4.1 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(2 x^{2} + 2 x + 2\right) ( x^{5} + x^{2} + 1 ) + 2$ |
$2$ |
$5$ |
$2$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$[1,1,1,1,1]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + t + 1)$ |
$[1, 3]$ |
| 2.5.2.10a4.2 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(2 x^{2} + 2 x + 2\right) ( x^{5} + x^{2} + 1 ) + 6$ |
$2$ |
$5$ |
$2$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$[1,1,1,1,1]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{2} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + t + 1)$ |
$[1, 3]$ |
| 2.5.2.10a5.1 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + 2 x^{3} ( x^{5} + x^{2} + 1 ) + 2$ |
$2$ |
$5$ |
$2$ |
$10$ |
$C_2^4 : C_5$ (as 10T8) |
$5$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{5}$ |
$[1,1,1,1]^{5}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t^3$ |
$[1, 3]$ |
| 2.5.2.10a5.2 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + 2 x^{3} ( x^{5} + x^{2} + 1 ) + 4 x + 2$ |
$2$ |
$5$ |
$2$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$10$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{10}$ |
$[1,1,1,1]^{10}$ |
$[2,2,2]^{2}$ |
$[1,1,1]^{2}$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{3} + 2 t^{2} + 2 t\right) x + 4 t^{2} + 2$ |
$[1, 0]$ |
$[1]$ |
$z + t^3$ |
$[1, 3]$ |
| 2.5.2.10a6.1 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(2 x^{4} + 2 x^{2}\right) ( x^{5} + x^{2} + 1 ) + 2$ |
$2$ |
$5$ |
$2$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$[1,1,1,1,1]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t^{2} + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + t^2)$ |
$[1, 3]$ |
| 2.5.2.10a6.2 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(2 x^{4} + 2 x^{2}\right) ( x^{5} + x^{2} + 1 ) + 6$ |
$2$ |
$5$ |
$2$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2, 2]^{5}$ |
$[1,1,1,1,1]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t^{2} + 2\right) x + 6$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + t^2)$ |
$[1, 3]$ |
| 2.5.2.10a7.1 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 2\right) ( x^{5} + x^{2} + 1 ) + 2$ |
$2$ |
$5$ |
$2$ |
$10$ |
$C_2^4 : C_5$ (as 10T8) |
$5$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{5}$ |
$[1,1,1,1]^{5}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t^{3} + 2 t^{2} + 2 t + 2\right) x + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + t^3 + t^2 + t + 1)$ |
$[1, 3]$ |
| 2.5.2.10a7.2 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(2 x^{4} + 2 x^{3} + 2 x^{2} + 2 x + 2\right) ( x^{5} + x^{2} + 1 ) + 4 x^{2} + 2$ |
$2$ |
$5$ |
$2$ |
$10$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$10$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{10}$ |
$[1,1,1,1]^{10}$ |
$[2,2,2]^{2}$ |
$[1,1,1]^{2}$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(2 t^{4} + 2 t\right) x + 4 t + 2$ |
$[1, 0]$ |
$[1]$ |
$z + (t^4 + t^3 + t^2 + t + 1)$ |
$[1, 3]$ |
| 2.5.2.15a1.1 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + 2$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{5}$ |
$[2]^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.2 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + 10$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{5}$ |
$[2]^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 10$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.3 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + 4 x^{3} ( x^{5} + x^{2} + 1 ) + 2$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[1,1,1,1,2]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{3} + 4 t^{2} + 4 t\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.4 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + 4 x^{3} ( x^{5} + x^{2} + 1 ) + 10$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[1,1,1,1,2]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t + 4\right) x + 10$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.5 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + 4 x ( x^{5} + x^{2} + 1 ) + 2$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[1,1,1,1,2]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4 t + 4\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.6 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + 4 x ( x^{5} + x^{2} + 1 ) + 10$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[1,1,1,1,2]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4 t + 4\right) x + 10$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.7 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(4 x^{2} + 4 x\right) ( x^{5} + x^{2} + 1 ) + 2$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[1,1,1,1,2]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.8 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(4 x^{2} + 4 x\right) ( x^{5} + x^{2} + 1 ) + 10$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[1,1,1,1,2]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4\right) x + 10$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.9 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + 4 ( x^{5} + x^{2} + 1 ) + 2$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{5}$ |
$[2]^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 4 x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.10 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + 4 ( x^{5} + x^{2} + 1 ) + 10$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_{10}$ (as 10T1) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[3]^{5}$ |
$[2]^{5}$ |
$[\ ]$ |
$[\ ]$ |
$10$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + 4 x + 10$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.11 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(4 x^{3} + 4\right) ( x^{5} + x^{2} + 1 ) + 2$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[1,1,1,1,2]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.12 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(4 x^{3} + 4\right) ( x^{5} + x^{2} + 1 ) + 10$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[1,1,1,1,2]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t\right) x + 10$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.13 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(4 x + 4\right) ( x^{5} + x^{2} + 1 ) + 2$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[1,1,1,1,2]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4 t\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.14 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(4 x + 4\right) ( x^{5} + x^{2} + 1 ) + 10$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[1,1,1,1,2]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{3} + 4 t\right) x + 10$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.15 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(4 x^{2} + 4 x + 4\right) ( x^{5} + x^{2} + 1 ) + 2$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[1,1,1,1,2]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{2} + 4\right) x + 2$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.5.2.15a1.16 |
$10$ |
$( x^{5} + x^{2} + 1 )^{2} + \left(4 x^{2} + 4 x + 4\right) ( x^{5} + x^{2} + 1 ) + 10$ |
$2$ |
$5$ |
$2$ |
$15$ |
$C_2 \times (C_2^4 : C_5)$ (as 10T14) |
$5$ |
$1$ |
$[3]$ |
$[2]$ |
$[2, 2, 2, 2, 3]^{5}$ |
$[1,1,1,1,2]^{5}$ |
$[2,2,2,2]$ |
$[1,1,1,1]$ |
$2$ |
$t^{5} + t^{2} + 1$ |
$x^{2} + \left(4 t^{4} + 4 t^{2} + 4\right) x + 10$ |
$[2, 0]$ |
$[1]$ |
$z + 1$ |
$[1, 3]$ |
| 2.2.5.8a1.1 |
$10$ |
$( x^{2} + x + 1 )^{5} + 2$ |
$2$ |
$2$ |
$5$ |
$8$ |
$F_5$ (as 10T4) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$[\ ]_{5}^{4}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t^{2} + t + 1$ |
$x^{5} + 2$ |
$[0]$ |
$[2]$ |
$z^4 + z^3 + 1$ |
$[5]$ |
| 2.1.10.10a1.1 |
$10$ |
$x^{10} + 2 x + 2$ |
$2$ |
$1$ |
$10$ |
$10$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[\frac{6}{5}]$ |
$[\frac{1}{5}]$ |
$[\frac{6}{5}, \frac{6}{5}, \frac{6}{5}, \frac{6}{5}]_{5}^{4}$ |
$[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5}]_{5}^{4}$ |
$[\frac{6}{5},\frac{6}{5},\frac{6}{5}]^{4}$ |
$[\frac{1}{5},\frac{1}{5},\frac{1}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x + 2$ |
$[1, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 11]$ |
| 2.1.10.10a1.2 |
$10$ |
$x^{10} + 2 x^{2} + 2 x + 2$ |
$2$ |
$1$ |
$10$ |
$10$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{6}{5}]$ |
$[\frac{1}{5}]$ |
$[\frac{6}{5}, \frac{6}{5}, \frac{6}{5}, \frac{6}{5}]_{5}^{4}$ |
$[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5}]_{5}^{4}$ |
$[\frac{6}{5},\frac{6}{5},\frac{6}{5}]^{4}$ |
$[\frac{1}{5},\frac{1}{5},\frac{1}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{2} + 2 x + 2$ |
$[1, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 11]$ |
| 2.1.10.12a1.1 |
$10$ |
$x^{10} + 2 x^{3} + 2$ |
$2$ |
$1$ |
$10$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{8}{5}]$ |
$[\frac{3}{5}]$ |
$[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}]_{5}^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]_{5}^{4}$ |
$[\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 13]$ |
| 2.1.10.12a1.2 |
$10$ |
$x^{10} + 2 x^{6} + 2 x^{3} + 2$ |
$2$ |
$1$ |
$10$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[\frac{8}{5}]$ |
$[\frac{3}{5}]$ |
$[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}]_{5}^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]_{5}^{4}$ |
$[\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{6} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 13]$ |
| 2.1.10.12a1.3 |
$10$ |
$x^{10} + 2 x^{5} + 2 x^{3} + 2$ |
$2$ |
$1$ |
$10$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{8}{5}]$ |
$[\frac{3}{5}]$ |
$[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}]_{5}^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]_{5}^{4}$ |
$[\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{5} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 13]$ |
| 2.1.10.12a1.4 |
$10$ |
$x^{10} + 2 x^{6} + 2 x^{5} + 2 x^{3} + 2$ |
$2$ |
$1$ |
$10$ |
$12$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[\frac{8}{5}]$ |
$[\frac{3}{5}]$ |
$[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}]_{5}^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]_{5}^{4}$ |
$[\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{6} + 2 x^{5} + 2 x^{3} + 2$ |
$[3, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 13]$ |
| 2.1.10.14a1.1 |
$10$ |
$x^{10} + 2 x^{5} + 2$ |
$2$ |
$1$ |
$10$ |
$14$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$5$ |
$[2]$ |
$[1]$ |
$[2]_{5}^{4}$ |
$[1]_{5}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{5} + 2$ |
$[5, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 10]$ |
| 2.1.10.14a1.2 |
$10$ |
$x^{10} + 2 x^{5} + 6$ |
$2$ |
$1$ |
$10$ |
$14$ |
$F_{5}\times C_2$ (as 10T5) |
$4$ |
$5$ |
$[2]$ |
$[1]$ |
$[2]_{5}^{4}$ |
$[1]_{5}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{5} + 6$ |
$[5, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 20]$ |
| 2.1.10.14a1.3 |
$10$ |
$x^{10} + 2 x^{9} + 2 x^{5} + 2$ |
$2$ |
$1$ |
$10$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[1]$ |
$[\frac{6}{5}, \frac{6}{5}, \frac{6}{5}, \frac{6}{5}, 2]_{5}^{4}$ |
$[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5},1]_{5}^{4}$ |
$[\frac{6}{5},\frac{6}{5},\frac{6}{5},\frac{6}{5}]^{4}$ |
$[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 2 x^{5} + 2$ |
$[5, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 19]$ |
| 2.1.10.14a1.4 |
$10$ |
$x^{10} + 2 x^{9} + 2 x^{5} + 6$ |
$2$ |
$1$ |
$10$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[1]$ |
$[\frac{6}{5}, \frac{6}{5}, \frac{6}{5}, \frac{6}{5}, 2]_{5}^{4}$ |
$[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5},1]_{5}^{4}$ |
$[\frac{6}{5},\frac{6}{5},\frac{6}{5},\frac{6}{5}]^{4}$ |
$[\frac{1}{5},\frac{1}{5},\frac{1}{5},\frac{1}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 2 x^{5} + 6$ |
$[5, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 19]$ |
| 2.1.10.14a1.5 |
$10$ |
$x^{10} + 2 x^{7} + 2 x^{5} + 2$ |
$2$ |
$1$ |
$10$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[1]$ |
$[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}, 2]_{5}^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5},1]_{5}^{4}$ |
$[\frac{8}{5},\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{7} + 2 x^{5} + 2$ |
$[5, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 17]$ |
| 2.1.10.14a1.6 |
$10$ |
$x^{10} + 2 x^{7} + 2 x^{5} + 6$ |
$2$ |
$1$ |
$10$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[1]$ |
$[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}, 2]_{5}^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5},1]_{5}^{4}$ |
$[\frac{8}{5},\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{7} + 2 x^{5} + 6$ |
$[5, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 17]$ |
| 2.1.10.14a1.7 |
$10$ |
$x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{5} + 2$ |
$2$ |
$1$ |
$10$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[1]$ |
$[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}, 2]_{5}^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5},1]_{5}^{4}$ |
$[\frac{8}{5},\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{5} + 2$ |
$[5, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 17]$ |
| 2.1.10.14a1.8 |
$10$ |
$x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{5} + 6$ |
$2$ |
$1$ |
$10$ |
$14$ |
$((C_2^4 : C_5):C_4)\times C_2$ (as 10T29) |
$4$ |
$5$ |
$[2]$ |
$[1]$ |
$[\frac{8}{5}, \frac{8}{5}, \frac{8}{5}, \frac{8}{5}, 2]_{5}^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5},1]_{5}^{4}$ |
$[\frac{8}{5},\frac{8}{5},\frac{8}{5},\frac{8}{5}]^{4}$ |
$[\frac{3}{5},\frac{3}{5},\frac{3}{5},\frac{3}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{9} + 2 x^{7} + 2 x^{5} + 6$ |
$[5, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 17]$ |
| 2.1.10.16a1.1 |
$10$ |
$x^{10} + 2 x^{7} + 2$ |
$2$ |
$1$ |
$10$ |
$16$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{12}{5}]$ |
$[\frac{7}{5}]$ |
$[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ |
$[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{7} + 2$ |
$[7, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 2.1.10.16a1.2 |
$10$ |
$x^{10} + 2 x^{7} + 4 x^{4} + 2$ |
$2$ |
$1$ |
$10$ |
$16$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[\frac{12}{5}]$ |
$[\frac{7}{5}]$ |
$[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ |
$[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{7} + 4 x^{4} + 2$ |
$[7, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 2.1.10.16a1.3 |
$10$ |
$x^{10} + 2 x^{7} + 4 x^{3} + 2$ |
$2$ |
$1$ |
$10$ |
$16$ |
$(C_2^4 : C_5):C_4$ (as 10T25) |
$4$ |
$5$ |
$[\frac{12}{5}]$ |
$[\frac{7}{5}]$ |
$[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ |
$[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{7} + 4 x^{3} + 2$ |
$[7, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
| 2.1.10.16a1.4 |
$10$ |
$x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{3} + 2$ |
$2$ |
$1$ |
$10$ |
$16$ |
$(C_2^4 : C_5):C_4$ (as 10T24) |
$4$ |
$5$ |
$[\frac{12}{5}]$ |
$[\frac{7}{5}]$ |
$[\frac{12}{5}, \frac{12}{5}, \frac{12}{5}, \frac{12}{5}]_{5}^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5},\frac{7}{5}]_{5}^{4}$ |
$[\frac{12}{5},\frac{12}{5},\frac{12}{5}]^{4}$ |
$[\frac{7}{5},\frac{7}{5},\frac{7}{5}]^{4}$ |
$2$ |
$t + 1$ |
$x^{10} + 2 x^{7} + 4 x^{4} + 4 x^{3} + 2$ |
$[7, 0]$ |
$[4, 1]$ |
$z^8 + z^6 + 1,z + 1$ |
$[5, 15]$ |
