What is the range of the Weierstrass elliptic function?

Question

There is the following function: $$ \wp(z,\Lambda):=\frac{1}{z^2} + \sum_{\lambda\in\Lambda\setminus\{0\}}\left(\frac 1 {(z-\lambda)^2} - \frac 1 {\lambda^2}\right) $$ What values can it take? For me it seems like it smoothly sweeps through the whole complex plane while it reaches infinity. It could be a certain shape how it stretches between zero and infinity, but as I see it covers the whole complex plane. Is it true? I did not find anything about what is the map of the fundamental region of this function.