Number of Poles in a Period Parallelogram

Question

The Weierstrass $\wp$ function has a double pole on every period. Its derivative $\wp'$ then has a triple pole on each period. Can I conclude that the quotient function $\dfrac{\wp'}{\wp}$ has a simple pole on each period? Is there any other poles for this function.

Answer 1

A function from an elliptic curve to the projective line cannot have a covering degree of $1$ (it would be a isomorphism). Note that $\wp$ also has two zeroes in each period.