Relation between Weierstrass zeta function and Weierstrass sigma function

Question

Given a $2d$ lattice $\mathbb{\Omega}$ in $\mathbb{C}$ and $ [x],[y] \in \mathbb{C}/ \mathbb{\Omega} $, where $[x] \neq \pm [y]$, define $f(z) = \zeta_\mathbb{\Omega}(x)+\zeta_\mathbb{\Omega}(y)+\zeta_\mathbb{\Omega}(z)-\zeta_\mathbb{\Omega}(x+y+z),$ where $\zeta_\mathbb{\Omega}(z)$ is the Weierstrass zeta function for $\mathbb{\Omega}$ . I have figured out that the zeros of $f$ are $(-x+\mathbb{\Omega}) \cup(-y+\mathbb{\Omega})$ and the poles of $f$ are $(-x-y+\mathbb{\Omega}) \cup\mathbb{\Omega}$, hence $f(z)=a \cdot \frac{\sigma_\Omega(y+z)\sigma_\Omega(x+z)}{\sigma_\Omega(z)\sigma_\Omega(x+y+z)}$ for some constant $a$ independent of $z$. Here $\sigma_\Omega(z)$ is the Weierstrass $\sigma $ function. How can I determine what $a$ is ? Many thanks in advance.