783 Elliptic Curves Spring 2013 Lecture # 23 05 / 07 / 2013

Let E/k be an elliptic curve with CM by an order O of discriminant D in an imaginary quadratic field K, and let ` be a prime not equal to the characteristic of k. The roots of Φ`(j(E), Y ) correspond to ` + 1 distinct `-isogenies from E to elliptic curves E′, not all of which may be defined over k; this depends on whether the roots lie in k or a proper… (More)