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§6. Periods Associated with Elliptic Curves: Elliptic Integrals 187
The torus can be obtained by opening up the slits ∞, e 1 and e 3 , e 2 in the two planes
and identifying opposite edges of the slits.
The left-hand parallelogram maps to the bottom half of the torus, the right-hand
parallelogram to the top half of the torus, the bottom half parallelogram to the front
of the torus, and the top half paralellogram to the back of the torus.
The reader is invited to express the arclength of the ellipse in terms of the inte-
grals in this section.
