Complex Multiplication of $y^2=x^3+B$

Question

I would like to find out what the complex endomorphism for the class of elliptic curves given by $$y^2=x^3+B$$ looks like.

I know that for the class of elliptic curves $$y^2=x^3+Ax,$$ the complex endomorphism is simply $(x,y)\mapsto(-x,iy)$. So what is the corresponding one for $y^2=x^3+B$?

Answer 1

Map x to $\zeta x $ where $\zeta $ is a third root of unity, and do nothing to $ y $.