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Arithmetic on Elliptic Curves with Complex Multiplication

โœ Scribed by Gross B.H.

Book ID
127448791
Year
1980
Tongue
English
Weight
6 MB
Category
Library

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Let E be an elliptic curve defined over Q and P โˆˆ E(Q) a rational point of infinite order. Suppose that E has complex multiplication by an order in the imaginary quadratic field k. Denote by M E,P the set of rational primes such that splits in k, E has good reduction at , and P is a primitive point

Complex Multiplication Structure of Elli
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Let k be a finite field and let E be an elliptic curve over k. In this paper we describe, for each finite extension l of k, the structure of the group E(l) of points of E over l as a module over the ring R of endomorphisms of E that are defined over k. If the Frobenius endomorphism ? of E over k doe