| 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 |
| 3.1.1.0a1.1 |
$1$ |
$x + 1$ |
$3$ |
$1$ |
$1$ |
$0$ |
Trivial (as 1T1) |
$1$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]$ |
$1$ |
$t + 1$ |
$x - 3$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 3.2.1.0a1.1 |
$2$ |
$x^{2} + 2 x + 2$ |
$3$ |
$2$ |
$1$ |
$0$ |
$C_2$ (as 2T1) |
$2$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t^{2} + 2 t + 2$ |
$x - 3$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 3.1.2.1a1.1 |
$2$ |
$x^{2} + 3$ |
$3$ |
$1$ |
$2$ |
$1$ |
$C_2$ (as 2T1) |
$1$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 1$ |
$x^{2} + 3$ |
$[0]$ |
$[1]$ |
$z + 2$ |
$[1]$ |
| 3.1.2.1a1.2 |
$2$ |
$x^{2} + 6$ |
$3$ |
$1$ |
$2$ |
$1$ |
$C_2$ (as 2T1) |
$1$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$2$ |
$t + 1$ |
$x^{2} + 6$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.3.1.0a1.1 |
$3$ |
$x^{3} + 2 x + 1$ |
$3$ |
$3$ |
$1$ |
$0$ |
$C_3$ (as 3T1) |
$3$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$[\ ]$ |
$[\ ]$ |
$3$ |
$t^{3} + 2 t + 1$ |
$x - 3$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 3.1.3.3a1.1 |
$3$ |
$x^{3} + 3 x + 3$ |
$3$ |
$1$ |
$3$ |
$3$ |
$S_3$ (as 3T2) |
$1$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$1$ |
$t + 1$ |
$x^{3} + 3 x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.1.3.3a1.2 |
$3$ |
$x^{3} + 6 x + 3$ |
$3$ |
$1$ |
$3$ |
$3$ |
$S_3$ (as 3T2) |
$1$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$1$ |
$t + 1$ |
$x^{3} + 6 x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.1.3.4a1.1 |
$3$ |
$x^{3} + 3 x^{2} + 3$ |
$3$ |
$1$ |
$3$ |
$4$ |
$S_3$ (as 3T2) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{2}$ |
$[1]^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$1$ |
$t + 1$ |
$x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[2]$ |
$z^2 + 1$ |
undefined |
| 3.1.3.4a2.1 |
$3$ |
$x^{3} + 6 x^{2} + 3$ |
$3$ |
$1$ |
$3$ |
$4$ |
$C_3$ (as 3T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$3$ |
$t + 1$ |
$x^{3} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 2$ |
undefined |
| 3.1.3.4a2.2 |
$3$ |
$x^{3} + 6 x^{2} + 12$ |
$3$ |
$1$ |
$3$ |
$4$ |
$C_3$ (as 3T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$3$ |
$t + 1$ |
$x^{3} + 6 x^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 2$ |
undefined |
| 3.1.3.4a2.3 |
$3$ |
$x^{3} + 6 x^{2} + 21$ |
$3$ |
$1$ |
$3$ |
$4$ |
$C_3$ (as 3T1) |
$1$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]$ |
$[1]$ |
$[\ ]$ |
$[\ ]$ |
$3$ |
$t + 1$ |
$x^{3} + 6 x^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 2$ |
undefined |
| 3.1.3.5a1.1 |
$3$ |
$x^{3} + 3$ |
$3$ |
$1$ |
$3$ |
$5$ |
$S_3$ (as 3T2) |
$1$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{5}{2}]_{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$1$ |
$t + 1$ |
$x^{3} + 3$ |
$[3, 0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.1.3.5a1.2 |
$3$ |
$x^{3} + 9 x + 3$ |
$3$ |
$1$ |
$3$ |
$5$ |
$S_3$ (as 3T2) |
$1$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{5}{2}]_{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$1$ |
$t + 1$ |
$x^{3} + 9 x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.1.3.5a1.3 |
$3$ |
$x^{3} + 18 x + 3$ |
$3$ |
$1$ |
$3$ |
$5$ |
$S_3$ (as 3T2) |
$1$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{5}{2}]_{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$1$ |
$t + 1$ |
$x^{3} + 18 x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.4.1.0a1.1 |
$4$ |
$x^{4} + 2 x^{3} + 2$ |
$3$ |
$4$ |
$1$ |
$0$ |
$C_4$ (as 4T1) |
$4$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{4} + 2 t^{3} + 2$ |
$x - 3$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 3.2.2.2a1.1 |
$4$ |
$( x^{2} + 2 x + 2 )^{2} + 3 x$ |
$3$ |
$2$ |
$2$ |
$2$ |
$C_4$ (as 4T1) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$[\ ]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + 2 t + 2$ |
$x^{2} + 3 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.2.2.2a1.2 |
$4$ |
$( x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$2$ |
$2$ |
$2$ |
$C_2^2$ (as 4T2) |
$2$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{2}$ |
$[\ ]_{2}^{2}$ |
$[\ ]$ |
$[\ ]$ |
$4$ |
$t^{2} + 2 t + 2$ |
$x^{2} + 3$ |
$[0]$ |
$[1]$ |
$z + 2$ |
$[1]$ |
| 3.1.4.3a1.1 |
$4$ |
$x^{4} + 3$ |
$3$ |
$1$ |
$4$ |
$3$ |
$D_{4}$ (as 4T3) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{4} + 3$ |
$[0]$ |
$[2]$ |
$z^3 + z^2 + 1$ |
$[2]$ |
| 3.1.4.3a1.2 |
$4$ |
$x^{4} + 6$ |
$3$ |
$1$ |
$4$ |
$3$ |
$D_{4}$ (as 4T3) |
$2$ |
$4$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{4}^{2}$ |
$[\ ]_{4}^{2}$ |
$[\ ]^{2}$ |
$[\ ]^{2}$ |
$2$ |
$t + 1$ |
$x^{4} + 6$ |
$[0]$ |
$[2]$ |
$z^3 + z^2 + 1$ |
undefined |
| 3.5.1.0a1.1 |
$5$ |
$x^{5} + 2 x + 1$ |
$3$ |
$5$ |
$1$ |
$0$ |
$C_5$ (as 5T1) |
$5$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{5}$ |
$[\ ]^{5}$ |
$[\ ]$ |
$[\ ]$ |
$5$ |
$t^{5} + 2 t + 1$ |
$x - 3$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 3.1.5.4a1.1 |
$5$ |
$x^{5} + 3$ |
$3$ |
$1$ |
$5$ |
$4$ |
$F_5$ (as 5T3) |
$4$ |
$5$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{5}^{4}$ |
$[\ ]_{5}^{4}$ |
$[\ ]^{4}$ |
$[\ ]^{4}$ |
$1$ |
$t + 1$ |
$x^{5} + 3$ |
$[0]$ |
$[4]$ |
$z^4 + 2 z^3 + z^2 + z + 2$ |
undefined |
| 3.6.1.0a1.1 |
$6$ |
$x^{6} + 2 x^{4} + x^{2} + 2 x + 2$ |
$3$ |
$6$ |
$1$ |
$0$ |
$C_6$ (as 6T1) |
$6$ |
$1$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]^{6}$ |
$[\ ]^{6}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{6} + 2 t^{4} + t^{2} + 2 t + 2$ |
$x - 3$ |
$[0]$ |
$[\ ]$ |
|
undefined |
| 3.3.2.3a1.1 |
$6$ |
$( x^{3} + 2 x + 1 )^{2} + 3 x$ |
$3$ |
$3$ |
$2$ |
$3$ |
$C_6$ (as 6T1) |
$3$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{3}$ |
$[\ ]_{2}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{3} + 2 t + 1$ |
$x^{2} + 3 t$ |
$[0]$ |
$[1]$ |
$z + 2$ |
undefined |
| 3.3.2.3a1.2 |
$6$ |
$( x^{3} + 2 x + 1 )^{2} + 3$ |
$3$ |
$3$ |
$2$ |
$3$ |
$C_6$ (as 6T1) |
$3$ |
$2$ |
$[\ ]$ |
$[\ ]$ |
$[\ ]_{2}^{3}$ |
$[\ ]_{2}^{3}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{3} + 2 t + 1$ |
$x^{2} + 3$ |
$[0]$ |
$[1]$ |
$z + 2$ |
$[1]$ |
| 3.2.3.6a1.1 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 6 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$3$ |
$6$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2}]_{2}^{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$2$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 6 x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t + 2)$ |
undefined |
| 3.2.3.6a2.1 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 3 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$3$ |
$6$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2}]_{2}^{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$2$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 3 x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t + 1)$ |
undefined |
| 3.2.3.6a3.1 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 6 x ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$3$ |
$6$ |
$C_3^2:C_4$ (as 6T10) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{2} + 2 t + 2$ |
$x^{3} + \left(3 t + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (t + 2)$ |
undefined |
| 3.2.3.6a4.1 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + \left(6 x + 6\right) ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$3$ |
$6$ |
$S_3^2$ (as 6T9) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{2} + 2 t + 2$ |
$x^{3} + \left(6 t + 6\right) x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + 1$ |
undefined |
| 3.2.3.6a5.1 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 3 x ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$3$ |
$6$ |
$C_3^2:C_4$ (as 6T10) |
$2$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}, \frac{3}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{1}{2}]_{2}^{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 3 t x + 3$ |
$[1, 0]$ |
$[1]$ |
$z + (2 t + 1)$ |
undefined |
| 3.2.3.8a1.1 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 3 ( x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$2$ |
$3$ |
$8$ |
$S_3$ (as 6T2) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{2}$ |
$[1]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 2$ |
undefined |
| 3.2.3.8a1.2 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 3 ( x^{2} + 2 x + 2 )^{2} + 9 x + 3$ |
$3$ |
$2$ |
$3$ |
$8$ |
$S_3\times C_3$ (as 6T5) |
$6$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{6}$ |
$[1]^{6}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 3 x^{2} + 9 t + 3$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 2$ |
undefined |
| 3.2.3.8a2.1 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 6 ( x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$2$ |
$3$ |
$8$ |
$C_6$ (as 6T1) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{2}$ |
$[1]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 6 x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 1$ |
undefined |
| 3.2.3.8a2.2 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 6 ( x^{2} + 2 x + 2 )^{2} + 12$ |
$3$ |
$2$ |
$3$ |
$8$ |
$C_6$ (as 6T1) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{2}$ |
$[1]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 6 x^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 1$ |
undefined |
| 3.2.3.8a2.3 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 6 ( x^{2} + 2 x + 2 )^{2} + 21$ |
$3$ |
$2$ |
$3$ |
$8$ |
$C_6$ (as 6T1) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2]^{2}$ |
$[1]^{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 6 x^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
$z^2 + 1$ |
undefined |
| 3.2.3.8a3.1 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 3 x ( x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$2$ |
$3$ |
$8$ |
$C_3^2:C_4$ (as 6T10) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{4}$ |
$[1,1]^{4}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$1$ |
$t^{2} + 2 t + 2$ |
$x^{3} + \left(6 t + 3\right) x^{2} + 3$ |
$[2, 0]$ |
$[2]$ |
$z^2 + 2 t$ |
undefined |
| 3.2.3.8a4.1 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + \left(3 x + 3\right) ( x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$2$ |
$3$ |
$8$ |
$S_3\times C_3$ (as 6T5) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{2}$ |
$[1,1]^{2}$ |
$[2]$ |
$[1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{3} + \left(3 t + 3\right) x^{2} + 12$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (2 t + 2)$ |
undefined |
| 3.2.3.8a4.2 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + \left(3 x + 3\right) ( x^{2} + 2 x + 2 )^{2} + 12$ |
$3$ |
$2$ |
$3$ |
$8$ |
$S_3\times C_3$ (as 6T5) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{2}$ |
$[1,1]^{2}$ |
$[2]$ |
$[1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{3} + \left(3 t + 3\right) x^{2} + 21$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (2 t + 2)$ |
undefined |
| 3.2.3.8a4.3 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + \left(3 x + 3\right) ( x^{2} + 2 x + 2 )^{2} + 21$ |
$3$ |
$2$ |
$3$ |
$8$ |
$S_3\times C_3$ (as 6T5) |
$2$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{2}$ |
$[1,1]^{2}$ |
$[2]$ |
$[1]$ |
$3$ |
$t^{2} + 2 t + 2$ |
$x^{3} + \left(6 t + 6\right) x^{2} + 3$ |
$[2, 0]$ |
$[1]$ |
$z^2 + (2 t + 2)$ |
undefined |
| 3.2.3.8a5.1 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 6 x ( x^{2} + 2 x + 2 )^{2} + 3$ |
$3$ |
$2$ |
$3$ |
$8$ |
$C_3^2:C_4$ (as 6T10) |
$4$ |
$1$ |
$[2]$ |
$[1]$ |
$[2, 2]^{4}$ |
$[1,1]^{4}$ |
$[2]^{2}$ |
$[1]^{2}$ |
$1$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 6 t x^{2} + 3$ |
$[2, 0]$ |
$[2]$ |
$z^2 + t$ |
undefined |
| 3.2.3.10a1.1 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 3$ |
$3$ |
$2$ |
$3$ |
$10$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{5}{2}]_{2}^{2}$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$2$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 3$ |
$[3, 0]$ |
$[1]$ |
$z + (2 t + 2)$ |
undefined |
| 3.2.3.10a1.2 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 9 x ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$3$ |
$10$ |
$S_3^2$ (as 6T9) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 9 t x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + (2 t + 2)$ |
undefined |
| 3.2.3.10a1.3 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 9 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$3$ |
$10$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{5}{2}]_{2}^{2}$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$2$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 9 x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + (2 t + 2)$ |
undefined |
| 3.2.3.10a1.4 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + \left(9 x + 9\right) ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$3$ |
$10$ |
$S_3^2$ (as 6T9) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{2} + 2 t + 2$ |
$x^{3} + \left(9 t + 9\right) x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + (2 t + 2)$ |
undefined |
| 3.2.3.10a1.5 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + 18 ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$3$ |
$10$ |
$D_{6}$ (as 6T3) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{5}{2}]_{2}^{2}$ |
$[\frac{3}{2}]_{2}^{2}$ |
$[\ ]_{2}$ |
$[\ ]_{2}$ |
$2$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 18 x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + (2 t + 2)$ |
undefined |
| 3.2.3.10a1.6 |
$6$ |
$( x^{2} + 2 x + 2 )^{3} + \left(9 x + 18\right) ( x^{2} + 2 x + 2 ) + 3$ |
$3$ |
$2$ |
$3$ |
$10$ |
$S_3^2$ (as 6T9) |
$2$ |
$2$ |
$[\frac{5}{2}]$ |
$[\frac{3}{2}]$ |
$[\frac{3}{2}, \frac{5}{2}]_{2}^{2}$ |
$[\frac{1}{2},\frac{3}{2}]_{2}^{2}$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$1$ |
$t^{2} + 2 t + 2$ |
$x^{3} + 18 t x + 3$ |
$[3, 0]$ |
$[1]$ |
$z + (2 t + 2)$ |
undefined |
| 3.1.6.6a1.1 |
$6$ |
$x^{6} + 3 x + 3$ |
$3$ |
$1$ |
$6$ |
$6$ |
$C_3^2:D_4$ (as 6T13) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\frac{5}{4}]^{2}_{2}$ |
$[\frac{1}{4}]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{6} + 3 x + 3$ |
$[1, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z + 2$ |
$[1, 4]$ |
| 3.1.6.6a1.2 |
$6$ |
$x^{6} + 3 x + 6$ |
$3$ |
$1$ |
$6$ |
$6$ |
$C_3^2:D_4$ (as 6T13) |
$2$ |
$4$ |
$[\frac{5}{4}]$ |
$[\frac{1}{4}]$ |
$[\frac{5}{4}, \frac{5}{4}]_{4}^{2}$ |
$[\frac{1}{4},\frac{1}{4}]_{4}^{2}$ |
$[\frac{5}{4}]^{2}_{2}$ |
$[\frac{1}{4}]^{2}_{2}$ |
$1$ |
$t + 1$ |
$x^{6} + 3 x + 6$ |
$[1, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z + 1$ |
undefined |
| 3.1.6.7a1.1 |
$6$ |
$x^{6} + 3 x^{2} + 3$ |
$3$ |
$1$ |
$6$ |
$7$ |
$S_3$ (as 6T2) |
$1$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t + 1$ |
$x^{6} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
$[1, 5]$ |
| 3.1.6.7a1.2 |
$6$ |
$x^{6} + 3 x^{3} + 3 x^{2} + 3$ |
$3$ |
$1$ |
$6$ |
$7$ |
$S_3\times C_3$ (as 6T5) |
$3$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}^{3}$ |
$[\frac{1}{2}]_{2}^{3}$ |
$[\ ]^{3}$ |
$[\ ]^{3}$ |
$3$ |
$t + 1$ |
$x^{6} + 3 x^{3} + 3 x^{2} + 3$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
$[1, 5]$ |
| 3.1.6.7a1.3 |
$6$ |
$x^{6} + 6 x^{2} + 6$ |
$3$ |
$1$ |
$6$ |
$7$ |
$S_3$ (as 6T2) |
$1$ |
$2$ |
$[\frac{3}{2}]$ |
$[\frac{1}{2}]$ |
$[\frac{3}{2}]_{2}$ |
$[\frac{1}{2}]_{2}$ |
$[\ ]$ |
$[\ ]$ |
$6$ |
$t + 1$ |
$x^{6} + 6 x^{2} + 6$ |
$[2, 0]$ |
$[1, 1]$ |
$z^3 + 2,2 z^2 + 1$ |
undefined |
