| 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 |
| 3.9.1.0a1.1 |
$9$ |
$x^{9} + 2 x^{3} + 2 x^{2} + x + 1$ |
$3$ |
$9$ |
$1$ |
$0$ |
$C_9$ (as 9T1) |
$9$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{9}$ |
$[\ ]^{9}$ |
$[\ ]$ |
$[\ ]$ |
$9$ |
$t^{9} + 2 t^{3} + 2 t^{2} + t + 1$ |
$x - 3$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 3.3.3.9a1.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 6 ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$9$ |
$S_3\times C_3$ (as 9T4) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2}]_{2}^{3}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 6 x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.3.3.9a2.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 3 ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$9$ |
$S_3\times C_3$ (as 9T4) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2}]_{2}^{3}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 3 x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.3.3.9a3.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 6 x ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{3}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 6 t x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + 2 t$ |
undefined |
| 3.3.3.9a4.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 3 x ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{3}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + t$ |
undefined |
| 3.3.3.9a5.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 6 x^{2} ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{3}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 3 t + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + 2 t^{2}$ |
undefined |
| 3.3.3.9a6.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x\right) ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{3}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 3 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^{2} + t)$ |
undefined |
| 3.3.3.9a7.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 3\right) ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$9$ |
$C_3^2 : S_3 $ (as 9T13) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{3}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^{2} + t + 1)$ |
undefined |
| 3.3.3.9a8.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 3\right) ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$9$ |
$C_3^2 : S_3 $ (as 9T13) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{3}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^{2} + 1)$ |
undefined |
| 3.3.3.9a9.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x\right) ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{3}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 3 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^{2} + 2 t)$ |
undefined |
| 3.3.3.9a10.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x + 3\right) ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$9$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{3}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 6 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^{2} + 2 t + 1)$ |
undefined |
| 3.3.3.12a1.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 3 ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$3$ |
$12$ |
$S_3\times C_3$ (as 9T4) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{6}$ |
$[1]^{6}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[2]$ |
$z^{2} + 1$ |
undefined |
| 3.3.3.12a2.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 6 ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3^2$ (as 9T2) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{3}$ |
$[1]^{3}$ |
$[\ ]$ |
$[\ ]$ |
$9$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + 2$ |
undefined |
| 3.3.3.12a2.2 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 6 ( x^{3} + 2 x + 1 )^{2} + 9 x^{2} + 3$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9$ (as 9T1) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{3}$ |
$[1]^{3}$ |
$[\ ]$ |
$[\ ]$ |
$9$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 6 x^{2} + 9 t^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + 2$ |
undefined |
| 3.3.3.12a2.3 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 6 ( x^{3} + 2 x + 1 )^{2} + 18 x^{2} + 3$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9$ (as 9T1) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{3}$ |
$[1]^{3}$ |
$[\ ]$ |
$[\ ]$ |
$9$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 6 x^{2} + 18 t^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + 2$ |
undefined |
| 3.3.3.12a3.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 3 x ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{3}$ |
$[1,1,1]^{3}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t + 3\right) x^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + t$ |
undefined |
| 3.3.3.12a3.2 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 3 x ( x^{3} + 2 x + 1 )^{2} + 12$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{3}$ |
$[1,1,1]^{3}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t + 3\right) x^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + t$ |
undefined |
| 3.3.3.12a3.3 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 3 x ( x^{3} + 2 x + 1 )^{2} + 21$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{3}$ |
$[1,1,1]^{3}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t + 3\right) x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + t$ |
undefined |
| 3.3.3.12a4.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 6 x ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$3$ |
$12$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{6}$ |
$[1,1,1]^{6}$ |
$[2,2]^{2}$ |
$[1,1]^{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[2]$ |
$z^{2} + 2 t$ |
undefined |
| 3.3.3.12a5.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 3 x^{2} ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$3$ |
$12$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{6}$ |
$[1,1,1]^{6}$ |
$[2,2]^{2}$ |
$[1,1]^{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 3 t^{2} x^{2} + 3$ |
$[2, 0]$ |
$[2]$ |
$z^{2} + t^{2}$ |
undefined |
| 3.3.3.12a6.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x\right) ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$3$ |
$12$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{6}$ |
$[1,1,1]^{6}$ |
$[2,2]^{2}$ |
$[1,1]^{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 3 t\right) x^{2} + 3$ |
$[2, 0]$ |
$[2]$ |
$z^{2} + (t^{2} + 2 t)$ |
undefined |
| 3.3.3.12a7.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9:C_3$ (as 9T6) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{3}$ |
$[1,1]^{3}$ |
$[2]$ |
$[1]$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 6 t + 6\right) x^{2} + 18 t + 3$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + (t^{2} + 2 t + 2)$ |
undefined |
| 3.3.3.12a7.2 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 9 x + 3$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3^2:C_3$ (as 9T7) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{3}$ |
$[1,1]^{3}$ |
$[2]$ |
$[1]$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 3 t + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + (t^{2} + 2 t + 2)$ |
undefined |
| 3.3.3.12a7.3 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(3 x^{2} + 6 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 18 x + 3$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_9:C_3$ (as 9T6) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{3}$ |
$[1,1]^{3}$ |
$[2]$ |
$[1]$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(3 t^{2} + 3\right) x^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + (t^{2} + 2 t + 2)$ |
undefined |
| 3.3.3.12a8.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3^2 : S_3 $ (as 9T13) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{6}$ |
$[1,1]^{6}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[2]$ |
$z^{2} + (2 t^{2} + 2)$ |
undefined |
| 3.3.3.12a9.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x\right) ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{3}$ |
$[1,1,1]^{3}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + (2 t^{2} + t)$ |
undefined |
| 3.3.3.12a9.2 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x\right) ( x^{3} + 2 x + 1 )^{2} + 12$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{3}$ |
$[1,1,1]^{3}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6 t\right) x^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + (2 t^{2} + t)$ |
undefined |
| 3.3.3.12a9.3 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x\right) ( x^{3} + 2 x + 1 )^{2} + 21$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{3}$ |
$[1,1,1]^{3}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 3 t\right) x^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + (2 t^{2} + t)$ |
undefined |
| 3.3.3.12a10.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{3}$ |
$[1,1,1]^{3}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 3 t + 6\right) x^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + (2 t^{2} + t + 2)$ |
undefined |
| 3.3.3.12a10.2 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 12$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{3}$ |
$[1,1,1]^{3}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + (2 t^{2} + t + 2)$ |
undefined |
| 3.3.3.12a10.3 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{3} + 2 x + 1 )^{2} + 21$ |
$3$ |
$3$ |
$3$ |
$12$ |
$C_3 \wr C_3 $ (as 9T17) |
$3$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{3}$ |
$[1,1,1]^{3}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(6 t^{2} + 6 t + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^{2} + (2 t^{2} + t + 2)$ |
undefined |
| 3.3.3.15a1.1 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 3$ |
$3$ |
$3$ |
$3$ |
$15$ |
$S_3\times C_3$ (as 9T4) |
$3$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{5}{2}]_{2}^{3}$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 3$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.3.3.15a1.2 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 9 x^{2} ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$15$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 9 t^{2} x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.3.3.15a1.3 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 18 x^{2} ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$15$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 18 t^{2} x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.3.3.15a1.4 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 9 x ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$15$ |
$C_3^2 : S_3 $ (as 9T13) |
$3$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{5}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{3}{2}]_{2}^{3}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(9 t + 9\right) x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.3.3.15a1.5 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 18 x ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$15$ |
$C_3^2 : S_3 $ (as 9T13) |
$3$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{5}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{3}{2}]_{2}^{3}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(18 t + 18\right) x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.3.3.15a1.6 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 9 ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$15$ |
$S_3\times C_3$ (as 9T4) |
$3$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{5}{2}]_{2}^{3}$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 9 x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.3.3.15a1.7 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(9 x^{2} + 9\right) ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$15$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(9 t^{2} + 9 t + 18\right) x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.3.3.15a1.8 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(18 x^{2} + 9\right) ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$15$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(18 t^{2} + 18 t\right) x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.3.3.15a1.9 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + 18 ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$15$ |
$S_3\times C_3$ (as 9T4) |
$3$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{5}{2}]_{2}^{3}$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x^{3} + 18 x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.3.3.15a1.10 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(9 x^{2} + 18\right) ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$15$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(9 t^{2} + 18 t\right) x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.3.3.15a1.11 |
$9$ |
$( x^{3} + 2 x + 1 )^{3} + \left(18 x^{2} + 18\right) ( x^{3} + 2 x + 1 ) + 3$ |
$3$ |
$3$ |
$3$ |
$15$ |
$(C_3^3:C_3):C_2$ (as 9T22) |
$3$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{5}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2},\frac{3}{2}]_{2}^{3}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{3} + 2 t + 1$ |
$x^{3} + \left(18 t^{2} + 18 t + 9\right) x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.1.9.9a1.1 |
$9$ |
$x^{9} + 3 x + 3$ |
$3$ |
$1$ |
$9$ |
$9$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[\frac{9}{8}, \frac{9}{8}]$ |
$[\frac{1}{8},\frac{1}{8}]$ |
$[\frac{9}{8}, \frac{9}{8}]_{8}^{2}$ |
$[\frac{1}{8},\frac{1}{8}]_{8}^{2}$ |
$[\ ]^{2}_{8}$ |
$[\ ]^{2}_{8}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x + 3$ |
$[1, 1, 0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.1.9.9a1.2 |
$9$ |
$x^{9} + 6 x + 3$ |
$3$ |
$1$ |
$9$ |
$9$ |
$(C_3^2:C_8):C_2$ (as 9T19) |
$2$ |
$8$ |
$[\frac{9}{8}, \frac{9}{8}]$ |
$[\frac{1}{8},\frac{1}{8}]$ |
$[\frac{9}{8}, \frac{9}{8}]_{8}^{2}$ |
$[\frac{1}{8},\frac{1}{8}]_{8}^{2}$ |
$[\ ]^{2}_{8}$ |
$[\ ]^{2}_{8}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x + 3$ |
$[1, 1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.1.9.10a1.1 |
$9$ |
$x^{9} + 3 x^{2} + 3$ |
$3$ |
$1$ |
$9$ |
$10$ |
$C_3^2:Q_8$ (as 9T14) |
$2$ |
$4$ |
$[\frac{5}{4}, \frac{5}{4}]$ |
$[\frac{1}{4},\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\ ]^{2}_{4}$ |
$[\ ]^{2}_{4}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x^{2} + 3$ |
$[2, 2, 0]$ |
$[2]$ |
$z^{2} + 1$ |
undefined |
| 3.1.9.10a2.1 |
$9$ |
$x^{9} + 6 x^{2} + 3$ |
$3$ |
$1$ |
$9$ |
$10$ |
$S_3^2:C_2$ (as 9T16) |
$2$ |
$4$ |
$[\frac{5}{4}, \frac{5}{4}]$ |
$[\frac{1}{4},\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\ ]^{2}_{4}$ |
$[\ ]^{2}_{4}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{2} + 3$ |
$[2, 2, 0]$ |
$[1]$ |
$z^{2} + 2$ |
undefined |
| 3.1.9.12a1.1 |
$9$ |
$x^{9} + 6 x^{4} + 3$ |
$3$ |
$1$ |
$9$ |
$12$ |
$C_3^2:C_4$ (as 9T9) |
$2$ |
$2$ |
$[\frac{3}{2}, \frac{3}{2}]$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{2}$ |
$[\ ]^{2}_{2}$ |
$[\ ]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{4} + 3$ |
$[4, 4, 0]$ |
$[2]$ |
$z^{4} + 1$ |
undefined |
| 3.1.9.12a2.1 |
$9$ |
$x^{9} + 3 x^{4} + 3$ |
$3$ |
$1$ |
$9$ |
$12$ |
$S_3^2$ (as 9T8) |
$2$ |
$2$ |
$[\frac{3}{2}, \frac{3}{2}]$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{2}$ |
$[\ ]^{2}_{2}$ |
$[\ ]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 3 x^{4} + 3$ |
$[4, 4, 0]$ |
$[2]$ |
$z^{4} + 2$ |
undefined |
| 3.1.9.12a3.1 |
$9$ |
$x^{9} + 6 x^{4} + 3 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$12$ |
$C_3^2 : C_6$ (as 9T11) |
$3$ |
$2$ |
$[\frac{3}{2}, \frac{3}{2}]$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{3}$ |
$[\ ]^{3}_{2}$ |
$[\ ]^{3}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{4} + 3 x^{3} + 3$ |
$[4, 3, 0]$ |
$[3]$ |
$z^{4} + 2 z + 1$ |
undefined |
| 3.1.9.12a3.2 |
$9$ |
$x^{9} + 6 x^{4} + 6 x^{3} + 3$ |
$3$ |
$1$ |
$9$ |
$12$ |
$C_3^2 : C_6$ (as 9T11) |
$3$ |
$2$ |
$[\frac{3}{2}, \frac{3}{2}]$ |
$[\frac{1}{2},\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{3}$ |
$[\ ]^{3}_{2}$ |
$[\ ]^{3}_{2}$ |
$1$ |
$t + 1$ |
$x^{9} + 6 x^{4} + 6 x^{3} + 3$ |
$[4, 3, 0]$ |
$[3]$ |
$z^{4} + z + 1$ |
undefined |
