j？？不变量生成 Hilbert 类域的简单证明
A simple proof of ？？j？？ invariant generates the Hilbert class field

Silverman证明了如下定理: 设？？K？？是一个虚二次域, ？？E？？是定义在复数域上的一条带复乘的椭圆曲线,其自同态环为？А？WTHT1〗O？？K？？, 则？？K？У？Hilbert类域等于？？K(j)？？, 其中？？j？？是椭圆曲线？？E？У莫？j？Р槐淞？. 本文给出了该定理的一个简单证明.
Silverman proved the following theorem: Let ？？E？？ be an elliptic curve over 〖WTHZ〗C〖WTBZ〗 with complex multiplication ？А？WTHT1〗O？？K？？, where ？А？WTHT1〗O？？K？？ is the ring of integers of an imaginary quadratic field ？？K？？, then the Hilbert class field of ？？K？？ is generated by the ？？j？？ invariant of ？？E？？ over ？？K？？. In this paper we give a simple proof of this fundamental theorem