Passport invariants
| Degree: | $3$ |
| Monodromy group: | $S_3$ |
| Genus: | $0$ |
| Geometry type: | spherical |
| Primitive: | yes |
Conjugacy class data
The order and cycle type of an element in each of the conjugacy classes $C_0, C_1, C_{\infty}$ of the passport containing this orbit.
| Order | Partition |
| $3$ | $3$ |
| $2$ | $2, 1$ |
| $2$ | $2, 1$ |
Base field
Curve
| $\mathbb{P}^1$, with affine coordinate $x$ | |
|
$\displaystyle x^{3} t + \left(-3 x - 2\right)=0$
|
(smooth)
(planar)
Map
\(\displaystyle \phi(x) =\)
$\displaystyle 2 \frac{1}{4 x^{3} - 3 x + 1}$
\(\displaystyle \phi(t,x) = \, t\)
Embeddings
Each permutation triple in the orbit corresponds to an embedded Belyi map with coefficients in $\mathbb{C}$. The table below gives this correspondence.
| Embedding $\nu \mapsto \nu_i \in \mathbb{C}$ | Permutation triple | Dessin |
| $\text{not applicable (over $\mathbb{Q}$)}$ | $(1,2,3), (2,3), (1,2)$ | View Embedding |