The theta function on Weierstrass normal form

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We want to write down the theta function of the point on Weierstrass normal form.

Now, we can embed an elliptic curve to projective plane by$E=\mathbb{C}/(\tau\mathbb{Z}+\mathbb{Z})\to \mathbb{P}^2$ such as $z\mapsto ({\mathscr p}(z):{\mathscr p'}(z):1)$ where ${\mathscr p}$ is Weierstrass elliptic function.

On the other hand, we can embed an elliptic curve to $\mathbb{P}^3$ by theta function such as $z\mapsto (\theta_{00}(2z):\theta_{01}(2z):\theta_{10}(2z):\theta_{11}(2z))$ where $\theta_{ij}$ are auxiliary theta functions.

I want to translate from a point $(x:y:1)$ in Weierstrass form to a point in $\mathbb{P}^3$. In other words, we want to write down theta function using by Weierstrass functions.