  Let p be a prime and let C be a genus one curve over a number field k
representing an element of order dividing p in the Shafarevich-Tate group of
its Jacobian. We describe an algorithm which computes the set of D in the
Shafarevich-Tate group such that pD = C and obtains explicit models for these D
as curves in projective space. This leads to a practical algorithm for
performing 9-descents on elliptic curves over the rationals.
