source 2006 Doche--Icart--Kohel "Efficient scalar multiplication by isogeny decompositions", page 196, bottom display, plus elimination of common subexpressions
parameter a4
assume a4 = 4 a
compute A = X1^2
compute U = a4 ZZ1
compute B = A-4 U
compute C = A U
compute Z3 = (2 Y1)^2
compute X3 = B^2
compute Y3 = Y1 B(2(X3+32 C)+a(Z3-C))
compute ZZ3 = Z3^2