Restriction of Weierstrass $\wp$-function

Question

The general definition of the Weierstrass $\wp$-function involves the periods $\omega_1$ and $\omega_2$. But at many places, the authors define the $\wp$-function with only one parameter, the periods ratio $\tau = \omega_2/\omega_1$. The relation is $$ \wp(z; \tau) = \wp(z; \; \omega_1 = 1/2, \; \omega_2 = \tau/2). $$ Is it possible to get the general $\wp$-function $\wp(z; \; \omega_1, \; \omega_2)$ from the "restriction" $\wp(z; \tau)$ ?

Answer 1

I've finally found the answer:: $$ \wp(z; \; \omega_1/2, \; \omega_2/2) = \wp(z/\omega_1; \tau) / \omega_1^2. $$