(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 at passes through , and deduce that is a point of order 4 in the group law.
(2) Let 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 .
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!