How do I compute the image of the cusp 0 on a modular elliptic curve?

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Using the modular parameterization we can get a q-series representation of the map from the upper half plane to the elliptic curve that sends the cusp infinity to the identity of the elliptic curve. However, plugging 0 into this q-series amounts to setting q=1 and the series does not converge. Is there a way to compute the image of 0 in E?