= Solution
The total pole order in one period cell is two, so the map has degree two. The <Riemann-Hurwitz formula> for <genus> one to <genus> zero gives $0=2\cdot2-R$, hence $R=4$. Each <local degree> is at most two, so every ramification contribution is exactly one. Therefore
$$
\boxed{\deg\wp=2,\qquad\text{four ramification points}.}
$$
They are zero and the three nonzero half-period classes. Zero is ramified because its reciprocal has a double zero. At a nonzero half-period, oddness and periodicity of $\wp'$ force $\wp'=0$; the count shows these exhaust the remaining points.
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