The definition height of a rational point on an elliptic curve which is not in Weierstrass normal form

Question

Assume that $$E:y^2 = x^3 + Ax + B$$ is an elliptic curve that is defined over ${\bf{Q}}$ and is expressed in Weierstrass form. Then, the height $H(P)$ of a rational point $P=({\frac{a}{b}},{\frac{c}{d}})\in{E({\bf{Q}})}$ is defined to be $$H(P) = {\rm{max}}(|a|,|b|).$$ Can this definition still be used to find the height of rational point of the curves not in Weierstrass normal form? Apologies if this is trivial! I can be more specific. If the elliptic curve is defined over ${\bf Q}$ as $$E:y^2 -y =2(x^3 -x),$$ how can find the height of a rational point on this curve? Do I first convert this curve to Weierstrass form and then use the definition above, or can I use the definition directly?