No abstract

Abstract. Let E be an elliptic curve over Q and p be a prime of good supersingular reduction for E. Although the Iwasawa theory of E over the cyclotomic Zp-extension of Q is well known to be fundamentally different from the case of good ordinary reduction at p, we are able to combine the method of our earlier paper with the theory of Kobayashi [5] and Pollack [8], to give an explicit upper bound for the number of copies of Qp/Zp occurring in the p-primary part of the Tate-Shafarevich group of E over Q.