Passport invariants
| Degree: | $3$ |
| Monodromy group: | $C_3$ |
| 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 |
| $3$ | $3$ |
| $3$ | $3$ |
| $1$ | $1, 1, 1$ |
Base field
Curve
| $\mathbb{P}^1$, with affine coordinate $x$ | |
|
$\displaystyle t + x^{3}=0$
|
(smooth)
(planar)
Map
\(\displaystyle \phi(x) =\)
$\displaystyle \frac{-1}{x^{3} - 1}$
\(\displaystyle \phi(t,x) = \, t\)
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 $\mathbb{Q}$)}$ | $(1,2,3), (1,3,2), ()$ | View Embedding |