Questions on elliptic curves

Question

Assignment:

Let E be the elliptic curve over F₅ defined by y² = x³+1.

Q1. Write down the division polynomial (ψ₃)(x) for this curve.
Q2. Show that the greatest common divisor of (ψ₃)(x) and "x^5 -x" is "x(x-1)."
Q3. Use Q(2) to show that the 3-torsion points in E(F₅) are {Origin,(0,1),(0,-1)}."

Provide complete and step by step solution for the question and show calculations and use formulas.