What is the divisor associated to this map?

Question

Suppose I have the map $\mathbb{P}^1 \to \mathbb{P}^2$ given by $(u,v) \mapsto (u^3, u^2v, v^3)$. What is the divisor associated to this map? I can't seem to figure it out. It seems the pullback of the $\infty$-divisor $V_+(z)$ is $(1,0)$ with multiplicity $3$. But then the map is given by $\mathcal{O}(3)$ which can't be true.

Answer 1

Semi-cubical parabolas along the z-axis , cubics along the x- axis ,

Answer 2

It is $\mathcal O_{\mathbb P^1}(3)$. The map is given by choosing the sub-basis $\{u^3, u^2v, v^3\}$ of $H^0(\mathcal O(3),\mathbb P^1)$.