The Arithmetic of Elliptic Curves with Complex Multiplication
نویسنده
چکیده
Introduction. Although it has occupied a central place in number theory for almost a century, the arithmetic of elliptic curves is still today a subject which is rich in conjectures, but sparse in definitive theorems. In this lecture, I will only discuss one main topic in the arithmetic of elliptic curves, namely the conjecture of Birch and Swinnerton-Dyer. We briefly recall how this conjecture arose (for more detailed accounts, see [1] and [5]). For simplicity, we shall only consider elliptic curves defined Dver the rational field Q. Let E be an elliptic curve defined over Q, which we can suppose to be given in Weierstrass normal form
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