# computing order of elliptic curves over binary field

Do you have any information on how to compute order of elliptic curves over binary field in SAGE mathematics software? Example: I have the following domain parameters which are taken from

```
p = 0800000000000000000000000000000000000000C9
a = 07B6882CAAEFA84F9554FF8428BD88E246D2782AE2
b = 0713612DCDDCB40AAB946BDA29CA91F73AF958AFD9
x = 0369979697AB43897789566789567F787A7876A654
y = 00435EDB42EFAFB2989D51FEFCE3C80988F41FF883
```

The problem I am facing is to to know the order of this elliptic curve? I ahve got on the net that it is possible to compute using this library sage.rings.finite_rings.finite_field_ext_pari.FiniteField_ext_pari and it takes these parameters properly with out any error. But there is error while requesting the order of that parameter.

This was what I deed in sage:

```
FF = sage.rings.finite_rings.finite_field_ext_pari.FiniteField_ext_pari;
order = 2**163;
c = 07B6882CAAEFA84F9554FF8428BD88E246D2782AE2;
b = 0713612DCDDCB40AAB946BDA29CA91F73AF958AFD9
K.<x>= GF(2)[];
K.<k> = FF(order, 'a', modulus = x^163 + x^7 + x^6 + x^3 + 1)[];
K163_curve = EllipticCurve(K,[1,c,0,0,b]);K163_curve
```

Our free book http://software.intel.com/en-us/articles/ipp-crypto-guide/ pages 264,265 contains some computations in C/C++ with "your" curve, including the order. We were not able to compute the order in Sage