Attack on Weierstrass Elliptic Curve

Question

I have a naive question(as non specialist in this field).

While reading Weierstrass Curve description,I found that it turns into 2 periodic tori on 2D complex plane. Is is it possible to create fast multiplication attack on this curve by implementing this transformation into tori on complex plain - like 2D clock multiplication by decomposing numbers into two dimention on complex plane? Here is something similar to this

• Elliptic Curves Lecture #17
• Complex Multiplication: Lecture 5