When complex multiplication(CM) is used to create elliptic curves over F

p

the ring of complex quadratic field is only used.The authors propose to use sub-ring of complex quadratic field to create elliptic curves over F

p

.Since the Pell equation u~2+dv

2

=4p exists root over Z/2p

Z/3p

more elliptic curves can then be created at the same range of discriminant.With the computation of Mathematica programming

the number of created curves increases significantly.