(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!