(1) Let y^2: = x^3+ 4x)" alt="Cy^2: = x^3+ 4x)" />, with the simplified group law (2.13) Show that the tangent line to C at P = (2,4) passes through (0,0), and deduce that P is a point of order 4 in the group law.

(2) Let C: (y^2=x^3+ax+b)\in \mathbb{R}^2 be nonsingular; find all points of order 2 in the group law, and understand what group they form (there are two cases to consider). Now explain geometrically how you would set about finding all points of order 4 on C.

I linked the text that we use in class above. If anyone can point me in the right direction or walk me through this, I would appreciate it. Thank you!