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of the two half-periods ω1 and ω2 of j, where j is defined in such a way that
is in the upper half-plane.
Note that the half-period ratio can be thought of as a simple number, namely, one of the parameters to elliptic functions, or it can be thought of as a function itself, because the half periods can be given in terms of the elliptic modulus or in terms of the nome.
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