Schwarz P with Neovius handles by Fujimori and Weber

Weierstrass Data

\[ M=\left\{(z,w)\in T\times(\mathbb{C}\cup\{\infty\})\;;\;w^4=\frac{\vartheta (z+p)^2\vartheta (z+q-\tau/2)^3}{\vartheta (z-p)^2\vartheta (z-q-\tau/2)^3}\right\}, \] where \[ \vartheta(z) =\vartheta(z,\tau) =\sum_{n=-\infty}^\infty e^{\pi i (n+1/2)^2\tau+2\pi i (n+1/2) (z-1/2)} \] is one of the classical Jacobi $\vartheta$-functions, $\tau$ is a pure imaginary number with $\mathrm{Im}(\tau)\gt 0$, $T=\mathbb{C}/\langle 1,\tau\rangle$ is the rectangular torus, and $p,q\in (0,1/2)$ are constants so that $4p+6q=1$. \[ g=w,\qquad \eta = \frac{dz}{w}. \] For given $\tau$, we can choose $p$ so that $f$ is single valued on $M$ as a map into $\mathbb{R}^3/\Lambda$, where $\Lambda=\{n_1\boldsymbol{v}_1+n_2\boldsymbol{v}_2+n_3\boldsymbol{v}_3\;;\;n_1,n_2,n_3\in\mathbb{Z}\}$ for some linearly independent vectors $\boldsymbol{v}_1,\boldsymbol{v}_2,\boldsymbol{v}_3\in\mathbb{R}^3$.