Arithmetic on elliptic curves with complex multiplication. II
β Scribed by Joe P. Buhler; Benedict H. Gross
- Publisher
- Springer-Verlag
- Year
- 1985
- Tongue
- English
- Weight
- 830 KB
- Volume
- 79
- Category
- Article
- ISSN
- 0020-9910
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let E be an elliptic curve defined over Q and P β 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
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
&163 ). We want to calculate the character sum where ( } Γp) is the Legendre symbol. We show that it is enough to calculate the sum for a finite number of primes and this has been done.