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Looking at Sloane's database, I found a neat formula for the lambda-invariant. Let $q:\tau \mapsto \exp(\pi i \tau)$ on the complex upper-half plane. Then

$\lambda(q) = 16q\;\prod_{k>0} \frac{(1 + q^{2k})^8}{(1 + q^{2k - 1})^8} = \frac{\vartheta_2(q)^4}{\vartheta_3(q)^4}.$

What are those theta functions?

I found this formula here.

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    If $y$ou need a pile of these coefficients, [Wolfram Alpha can handle that.](http://www.wolframalpha.com/input/?i=Table%5BSeriesCoefficient%5BInverseEllipticNomeQ%5Bq%5D%2C+%7Bq%2C+0%2C+k%7D%5D%2C+%7Bk%2C+0%2C+50%7D%5D)2011-10-22

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They are Jacobi theta functions (with $z=0$)

$\vartheta_2(q)=\sum_{n=-\infty}^{\infty} q^{(n+1/2)^2}, \qquad \vartheta_3(q)=\sum_{n=-\infty}^{\infty} q^{n^2}$