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 tried Sage. It took me around 3-4 hours to compile to x64 ubuntu. It seems to be a good program. But when the j-invariant is 0 the SEA algorithm can't be used, and then it seems to have some problems if you use large values for p/k.

After searching some more I also found miracl: http://www.shamus.ie/index.php?page=elliptic-curves They have implementations for both the normal Schoof and SEA algorithm. But this program also has some problems when using large input values. After 3-4 hours of running it crashed :/. I tried to fix it, and currently it's running again so hopefully it will work.

Edit: It works now. The program in the link above is identical to the one Rasmus Faber gave.