The Selmer Groups of Elliptic Curves

Let E / K be an elliptic curve with K-rational p-torsion points. The p-Selmer group of E is described by the image of a map λ _K and hence an upper bound of its order is given in terms of the class numbers of the S-ideal class group of K and the p-division field of E. Supported by the Natural Science Foundation of Peking University