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)
