Have (1-ydbl)/(1+ydbl)
= (y^2-1)/(ax^2-1)
Have (y^2-1)*(ax^2-1) = (a-d) x^2 y^2
==> (1-ydbl)/(1+ydbl) has same parity as a-d
No points at infinity => d nonsqr, ad nonsqr -> a sqr.
Point of order 8: ax^2=y^2
2y^2 = 1+day^4
product of roots = 1/ad = nonsquare, so one will be square (if no point at infty)
b^2-4ac = 4(1-ad) -> 1-ad square iff point of order 8 exists
If a^2 = 1, then 1-ad = a(a-d)