Elliptic Curves with Complex Multiplication and a Character Sum Original Research Article

Letf(x)set membership, variantimage[X] be a cubic such thaty2=f(x) is an elliptic curve with complex multiplication by[formula],[formula],[formula]or[formula]. We want to calculate the character sum[formula]where (·/p) 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.