Complex Elliptic Functions

[monomocoso]

If \(\displaystyle \beta_1\) and \(\displaystyle \beta_2\) are points inside the fundamental parallelogram with respective residues\(\displaystyle \alpha_1\) and \(\displaystyle \alpha_2\), let \(\displaystyle f(z)\) be an elliptic function with only two simple poles at \(\displaystyle z=\beta_1\) and \(\displaystyle z=\beta_2\). Express \(\displaystyle f\) in terms of the Weierstrass function \(\displaystyle \rho\) by considering the function
\(\displaystyle {\frac {A}{\rho(z-\beta)+B} +C}\)
How do you choose the constants \(\displaystyle A, B, C\), and \(\displaystyle \beta\) to construct \(\displaystyle f\)?