Weierstrass Elliptic Function and p-function

Question

Definitions

[(Simpler form of) Weierstrass elliptic function] In the projective space, it is an elliptic curve; $y^2z = x^3 + Axz^2 + Bz^3$

[Weierstrass p-function] In the projective space, it is a periodic function; $\wp(z, \omega_1, \omega_2) = \frac{1}{z^2} + \sum_{\lambda \in \Lambda - \{ 0 \}} (\frac{1}{(z - \lambda)^2} - \frac{1}{\lambda ^ 2})$

Question

Is the link between these two concepts in the differential equation of p-function, i.e.,

• $\wp'^2 = 4 \wp^3 + g_2 \wp + g_3$ for some functions $g_2, g_3$ and now this is taking the same form as Weierstrass elliptic function
• Elliptic function is, as in projective space, a "homogenised" version of this DE
  ?

Thank you for taking time to check my question!