It is easy to see that for any entire function f : ℂ → ℂ, its graph G(f) = {(z,f(z)) ∈ ℂ<sup>2</sup>  |  z ∈ ℂ} can be translated by (0,c) for any c ∈ ℂ, so that all the translated graphs {G(f) + (0,c)  |  c ∈ ℂ} form the leaves of a holomorphic foliation of ℂ<sup>2</sup>.

Is it known exactly which holomorphic curves X ⊂ ℂ<sup>2</sup> can be a leaf of a non-singular holomorphic foliation of ℂ<sup>2</sup>?