18.783 Elliptic Curves Spring 2013 Lecture #20 04/25/2013 20.1 The Hilbert class polynomial
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چکیده
Let O be an order of discriminant D in an imaginary quadratic field K. In Lecture 19 we saw that there is a one-to-one relationship between isomorphism classes of elliptic curves with complex multiplication by O (the set EllO(C)), and equivalence classes of proper Oideals (the group cl(O)). The first main theorem of complex multiplication states that the elements of EllO(C) are algebraic integers that all have the same minimal polynomial
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تاریخ انتشار 2013