Regarding the connected component of $|1/J| < 1$ containing $\infty$

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How does one explicitly describe the connected component of $|1/J| < 1$ containing $\infty$? Here, $J = J(\tau) = j(\tau)/12^3$ is the normalized $j$-invariant so that $J(i) = 1$, and $\tau$ is in the upper half-plane.