### Order of randomly generated elliptic curve

I was computing order of random elliptic curves over prime field with out any problem. But when it comes to computing order of elliptic curves over binary field(characteristic 2 field), it computes well for small values of a and b of the elliptic curve.
The problem comes when a and b parameters are large, specifically for 160 bit elliptic curve parameters. I can generate random point of the elliptic curve of 160 bits. However, when I compute its order, it displays, after a long run, exhaust memory and then it exits, and some times Jim dead.

I could not understand the problem. Could you say something for me regarding this problem? Thank you in advance.