# SAGE random point on elliptic curve with a specific order

I am playing around with SAGE and elliptic curves. Is there a way to pick a point at random on an elliptic curve with a specific order that I choose?

I use the function random_point(), but the order of the returned point is virtually random. Are there any smart way besides iteratively call random_point() until a point with the desired order is found?

Thanks! :D

E = EllipticCurve([1, 0, 0, -45, 81]);