| 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 |
| 3.12.1.0a1.1 |
$12$ |
$x^{12} + x^{6} + x^{5} + x^{4} + x^{2} + 2$ |
$3$ |
$12$ |
$1$ |
$0$ |
$C_{12}$ (as 12T1) |
$12$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{12}$ |
$[\ ]^{12}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{12} + t^{6} + t^{5} + t^{4} + t^{2} + 2$ |
$x - 3$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 3.6.2.6a1.1 |
$12$ |
$( x^{6} + 2 x^{4} + x^{2} + 2 x + 2 )^{2} + 3 x$ |
$3$ |
$6$ |
$2$ |
$6$ |
$C_{12}$ (as 12T1) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$[\ ]_{2}^{6}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{6} + 2 t^{4} + t^{2} + 2 t + 2$ |
$x^{2} + 3 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.6.2.6a1.2 |
$12$ |
$( x^{6} + 2 x^{4} + x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$6$ |
$2$ |
$6$ |
$C_6\times C_2$ (as 12T2) |
$6$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{6}$ |
$[\ ]_{2}^{6}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{6} + 2 t^{4} + t^{2} + 2 t + 2$ |
$x^{2} + 3$ |
$[0]$ |
$[1]$ |
$z + 2$ |
$[1]$ |
| 3.4.3.12a1.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 6 ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$S_3 \times C_4$ (as 12T11) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2}]_{2}^{4}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$4$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 6 x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + t^3$ |
undefined |
| 3.4.3.12a2.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 3 ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$S_3 \times C_4$ (as 12T11) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2}]_{2}^{4}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$4$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 3 x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + 2 t^3$ |
undefined |
| 3.4.3.12a3.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 6 x ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$F_9$ (as 12T46) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 6 t^{3} x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + 1)$ |
undefined |
| 3.4.3.12a4.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 3 x ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$F_9$ (as 12T46) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 6 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^3 + 2)$ |
undefined |
| 3.4.3.12a5.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 6 x^{2} ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^2:C_4\times S_3$ (as 12T119) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 6 t + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + t + 1)$ |
undefined |
| 3.4.3.12a6.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{2} + 3\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 6 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t + 1)$ |
undefined |
| 3.4.3.12a7.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{2} + 6 x + 3\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 6 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + t + 2)$ |
undefined |
| 3.4.3.12a8.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{2} + 6 x + 6\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t^{2} + 3 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + 2 t)$ |
undefined |
| 3.4.3.12a9.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{2} + 6 x + 3\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t^{2} + 3 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^3 + 2 t)$ |
undefined |
| 3.4.3.12a10.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{3} + 6\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^2:C_4\times S_3$ (as 12T119) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^3 + t^2 + t + 1)$ |
undefined |
| 3.4.3.12a11.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{3} + 6 x + 6\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t^{2} + 6 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + t + 2)$ |
undefined |
| 3.4.3.12a12.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{3} + 6 x + 3\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + t^2 + t + 2)$ |
undefined |
| 3.4.3.12a13.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{3} + 3 x\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 3 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + t)$ |
undefined |
| 3.4.3.12a14.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{3} + 6 x^{2} + 3\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_2\times C_3^2:C_4$ (as 12T41) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$2$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + t^2 + 2 t + 2)$ |
undefined |
| 3.4.3.12a15.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{3} + 6 x^{2} + 6 x + 3\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^2:C_4\times S_3$ (as 12T119) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^3 + t^2 + 2 t)$ |
undefined |
| 3.4.3.12a16.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{3} + 6 x^{2} + 3 x + 3\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t^{2}\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 2 t + 1)$ |
undefined |
| 3.4.3.12a17.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{3} + 3 x^{2} + 3 x + 6\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^3:(C_4\times S_3)$ (as 12T170) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^2 + 2)$ |
undefined |
| 3.4.3.12a18.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{3} + 3\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^2:C_4\times S_3$ (as 12T119) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t^{2} + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t^3 + 2 t^2 + 2 t + 2)$ |
undefined |
| 3.4.3.12a19.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{3} + 6 x^{2} + 6 x + 6\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 3 t + 3\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^3 + 2 t^2 + 1)$ |
undefined |
| 3.4.3.12a20.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{3} + 6 x^{2} + 3 x\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^3 + 2 t^2 + 2)$ |
undefined |
| 3.4.3.12a21.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{3} + 3 x^{2} + 6\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_2\times C_3^2:C_4$ (as 12T41) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$2$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^3 + 2 t^2 + t + 1)$ |
undefined |
| 3.4.3.12a22.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{3} + 3 x^{2} + 3\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_6.D_6$ (as 12T39) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$2$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^2 + t + 1)$ |
undefined |
| 3.4.3.12a23.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{3} + 3 x^{2} + 6 x + 6\right) ( x^{4} + 2 x^{3} + 2 ) + 3$ |
$3$ |
$4$ |
$3$ |
$12$ |
$C_3^2:F_9$ (as 12T173) |
$4$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}, \frac{3}{2}, \frac{3}{2}]_{2}^{4}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}^{4}$ |
$[\frac{3}{2},\frac{3}{2},\frac{3}{2}]_{2}$ |
$[\frac{1}{2},\frac{1}{2},\frac{1}{2}]_{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t^2 + t + 2)$ |
undefined |
| 3.4.3.16a1.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 3 ( x^{4} + 2 x^{3} + 2 )^{2} + 3$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3 : C_4$ (as 12T5) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{4}$ |
$[1]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (t^3 + t^2 + t + 1)$ |
undefined |
| 3.4.3.16a1.2 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 3 ( x^{4} + 2 x^{3} + 2 )^{2} + 9 x + 3$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3\times (C_3 : C_4)$ (as 12T19) |
$12$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{12}$ |
$[1]^{12}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$6$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 3 x^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (t^3 + t^2 + t + 1)$ |
undefined |
| 3.4.3.16a2.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 6 ( x^{4} + 2 x^{3} + 2 )^{2} + 3$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_{12}$ (as 12T1) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{4}$ |
$[1]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (2 t^3 + 2 t^2 + 2 t + 2)$ |
undefined |
| 3.4.3.16a2.2 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 6 ( x^{4} + 2 x^{3} + 2 )^{2} + 12$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_{12}$ (as 12T1) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{4}$ |
$[1]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 6 x^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (2 t^3 + 2 t^2 + 2 t + 2)$ |
undefined |
| 3.4.3.16a2.3 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 6 ( x^{4} + 2 x^{3} + 2 )^{2} + 21$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_{12}$ (as 12T1) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{4}$ |
$[1]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$12$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 6 x^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (2 t^3 + 2 t^2 + 2 t + 2)$ |
undefined |
| 3.4.3.16a3.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 3 x ( x^{4} + 2 x^{3} + 2 )^{2} + 3$ |
$3$ |
$4$ |
$3$ |
$16$ |
$F_9$ (as 12T46) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{8}$ |
$[1,1]^{8}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 6 t\right) x^{2} + 3$ |
$[2, 0]$ |
$[2]$ |
$z^2 + (2 t^3 + t^2 + t + 1)$ |
undefined |
| 3.4.3.16a4.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 6 x ( x^{4} + 2 x^{3} + 2 )^{2} + 3$ |
$3$ |
$4$ |
$3$ |
$16$ |
$F_9$ (as 12T46) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{8}$ |
$[1,1]^{8}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 3 t\right) x^{2} + 3$ |
$[2, 0]$ |
$[2]$ |
$z^2 + (t^3 + 2 t^2 + 2 t + 2)$ |
undefined |
| 3.4.3.16a5.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 3 x^{2} ( x^{4} + 2 x^{3} + 2 )^{2} + 3$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3^2:C_{12}$ (as 12T73) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{4}$ |
$[1,1,1]^{4}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 6 t + 3\right) x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (t^2 + t + 2)$ |
undefined |
| 3.4.3.16a5.2 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 3 x^{2} ( x^{4} + 2 x^{3} + 2 )^{2} + 12$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3^2:C_{12}$ (as 12T73) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{4}$ |
$[1,1,1]^{4}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + 3 t^{2} x^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (t^2 + t + 2)$ |
undefined |
| 3.4.3.16a5.3 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + 3 x^{2} ( x^{4} + 2 x^{3} + 2 )^{2} + 21$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3^2:C_{12}$ (as 12T73) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{4}$ |
$[1,1,1]^{4}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t^{2} + 6 t + 3\right) x^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (t^2 + t + 2)$ |
undefined |
| 3.4.3.16a6.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{2} + 6\right) ( x^{4} + 2 x^{3} + 2 )^{2} + 3$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3^2:F_9$ (as 12T173) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{8}$ |
$[1,1,1,1]^{8}$ |
$[2,2,2]^{2}$ |
$[1,1,1]^{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t^{2} + 3 t\right) x^{2} + 3$ |
$[2, 0]$ |
$[2]$ |
$z^2 + (2 t^3 + 1)$ |
undefined |
| 3.4.3.16a7.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{2} + 3 x + 6\right) ( x^{4} + 2 x^{3} + 2 )^{2} + 3$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{4}$ |
$[1,1,1,1]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$3$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t^{2} + 3 t\right) x^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (t^3 + t^2 + t + 2)$ |
undefined |
| 3.4.3.16a7.2 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{2} + 3 x + 6\right) ( x^{4} + 2 x^{3} + 2 )^{2} + 12$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{4}$ |
$[1,1,1,1]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$3$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t^{2} + 3 t\right) x^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (t^3 + t^2 + t + 2)$ |
undefined |
| 3.4.3.16a7.3 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{2} + 3 x + 6\right) ( x^{4} + 2 x^{3} + 2 )^{2} + 21$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{4}$ |
$[1,1,1,1]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$3$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{2} + 6 t + 3\right) x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (t^3 + t^2 + t + 2)$ |
undefined |
| 3.4.3.16a8.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{2} + 3 x + 3\right) ( x^{4} + 2 x^{3} + 2 )^{2} + 3$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3^2:F_9$ (as 12T173) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{8}$ |
$[1,1,1,1]^{8}$ |
$[2,2,2]^{2}$ |
$[1,1,1]^{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 3 t + 3\right) x^{2} + 3$ |
$[2, 0]$ |
$[2]$ |
$z^2 + (t^2 + t)$ |
undefined |
| 3.4.3.16a9.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{4} + 2 x^{3} + 2 )^{2} + 3$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{4}$ |
$[1,1,1,1]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$3$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 3 t + 6\right) x^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (t^3 + 2 t^2 + 2 t + 1)$ |
undefined |
| 3.4.3.16a9.2 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{4} + 2 x^{3} + 2 )^{2} + 12$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{4}$ |
$[1,1,1,1]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$3$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{2} + 6 t + 3\right) x^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (t^3 + 2 t^2 + 2 t + 1)$ |
undefined |
| 3.4.3.16a9.3 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(6 x^{2} + 3 x + 6\right) ( x^{4} + 2 x^{3} + 2 )^{2} + 21$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{4}$ |
$[1,1,1,1]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$3$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t^{2} + 6 t\right) x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (t^3 + 2 t^2 + 2 t + 1)$ |
undefined |
| 3.4.3.16a10.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{3} + 3\right) ( x^{4} + 2 x^{3} + 2 )^{2} + 3$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3^2:C_{12}$ (as 12T73) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{4}$ |
$[1,1,1]^{4}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t^{2} + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (2 t^3 + 2 t^2 + 1)$ |
undefined |
| 3.4.3.16a10.2 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{3} + 3\right) ( x^{4} + 2 x^{3} + 2 )^{2} + 12$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3^2:C_{12}$ (as 12T73) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{4}$ |
$[1,1,1]^{4}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t^{2} + 6\right) x^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (2 t^3 + 2 t^2 + 1)$ |
undefined |
| 3.4.3.16a10.3 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{3} + 3\right) ( x^{4} + 2 x^{3} + 2 )^{2} + 21$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3^2:C_{12}$ (as 12T73) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2]^{4}$ |
$[1,1,1]^{4}$ |
$[2,2]$ |
$[1,1]$ |
$3$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t + 3\right) x^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (2 t^3 + 2 t^2 + 1)$ |
undefined |
| 3.4.3.16a11.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{3} + 3 x + 3\right) ( x^{4} + 2 x^{3} + 2 )^{2} + 3$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3^2:F_9$ (as 12T173) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{8}$ |
$[1,1,1,1]^{8}$ |
$[2,2,2]^{2}$ |
$[1,1,1]^{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 3 t + 3\right) x^{2} + 3$ |
$[2, 0]$ |
$[2]$ |
$z^2 + (t^3 + t + 2)$ |
undefined |
| 3.4.3.16a12.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{3} + 3 x + 6\right) ( x^{4} + 2 x^{3} + 2 )^{2} + 3$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3^2:F_9$ (as 12T173) |
$8$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{8}$ |
$[1,1,1,1]^{8}$ |
$[2,2,2]^{2}$ |
$[1,1,1]^{2}$ |
$1$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(6 t^{3} + 6 t\right) x^{2} + 3$ |
$[2, 0]$ |
$[2]$ |
$z^2 + (2 t^3 + t^2 + 2 t)$ |
undefined |
| 3.4.3.16a13.1 |
$12$ |
$( x^{4} + 2 x^{3} + 2 )^{3} + \left(3 x^{3} + 6 x\right) ( x^{4} + 2 x^{3} + 2 )^{2} + 3$ |
$3$ |
$4$ |
$3$ |
$16$ |
$C_3\wr C_4$ (as 12T131) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2, 2, 2]^{4}$ |
$[1,1,1,1]^{4}$ |
$[2,2,2]$ |
$[1,1,1]$ |
$3$ |
$t^{4} + 2 t^{3} + 2$ |
$x^{3} + \left(3 t^{3} + 6 t\right) x^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (2 t^3 + t + 2)$ |
undefined |
