 Solution

ID: past-exam-of-the-geometry-course-of-the-university-of-oxford/2011/2/c/ii/solution

A pole occurs exactly when

2 z \in Λ

. Thus the poles on

T

are

[0], [ω_{1} /2], [ω_{2} /2], [(ω_{1} + ω_{2}) /2] .

Each is a double pole, since the multiplication-by-two map is locally unramified and

℘

[0]

. There are four distinct poles, each of order two, consistent with the degree eight.

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