As far as I can find out you do it by forcing the point you find to be in the kernel of the isogeny, apparently this is enough information to construct the codomain.
So basically if you've constructed point R you then simply require:
phi(P + R) = phi(P)
and see what kind of space you end up with. Apparently it'll still be an elliptic curve.
So basically if you've constructed point R you then simply require:
phi(P + R) = phi(P)
and see what kind of space you end up with. Apparently it'll still be an elliptic curve.