I am studying elliptic curves using this book and have a problem with task 4.11 which goes as follows:
Let $F_q$ be a finite field of odd characteristic and let $ a,b \in F_q $ with $a \ne2b$ and $b \ne 0. $ Define the elliptic curve E by $ y^2 = x^3+ax^2+b^2x $ a) Show that the points $ (b,b\sqrt{a+2b})$ and $(-b,-b\sqrt{a-2b}) $ have order 4.
So, if the curve was on normal weierstrass form I guess I could use the formula and eventually reach infinity, but if the curve can have characteristic 3, then how can I transform it to weierstrass? Or is there any other way to show that the points have order 4 using schoof's or baby-step giant-step etc?