Schwarz primitive family (triply periodic)

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$r=(\sqrt{3}-1)/\sqrt{2}$, $\theta =\pi/4$ (the most symmetric case).

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$r=0.9$, $\theta =\pi/4$.

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$r=0.9$, $\theta =3\pi/8$.

Weierstrass Data

\[ M=\big\{(z,w)\in(\mathbb{C}\cup\{\infty\})^2\;;\;w^2=(z^4-2r^2z^2\cos 2\theta+r^4)(z^4-2r^{-2}z^2\cos 2\theta+r^{-4})\big\}, \] where $r\in (0,1)$ and $\theta\in (0,\pi/2)$ are constants. \[ g=z,\qquad \eta = \frac{dz}{w}dz. \]