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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.

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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.

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  • $\begingroup$ Could you please elaborate more on that? Sorry I am new to the topic $\endgroup$ – Sekots Reivan Nov 9 '16 at 17:28

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