Standard curves, their properties, and an implementation 

1) Select an GF(2^k) curve and implement addition,
multiplication and inversion using: Maple, Matlab,
Mathematica, or C/C++

2) Select an GF(p) curve and implement addition,
multiplication and inversion using: Maple, Matlab,
Mathematica, or C/C++

See my papers and technical reports, on Montgomery 
multiplication mod p and GF(2^k)

See hankerson.pdf for implementation examples.