Number of points on elliptic curve

Question

If you have an elliptic curve in the form of:

y^2 = x^3 + a*x + b  (mod p)

Is there a good program to calculate the number of points on this cu

Answer 1

I have been using Mike Scotts program(miracl) for this purpose also. Being just curious may I ask: How large were the domains with prime group order you could produce with the software? I got up to 1024 bit and now quit because I need my office PC for something other than running point counting software for weeks on end. Did you produce larger domains? If so I would be glad to get the domain parameters and if you don't have objections would include them in my ECC-Software Academic Signature.

My domains can be found here ECC Domain Page. The software to use them with is accessible from here Manual with Link to download page

Regards.