Security, Math, Cryptography.
There are also a couple of interesting forms: the Weierstrass form: y = x³ + dx² + ex + f the extended Jacobi quartic form: y² = dx⁴ + 2ax² + 1 the twisted Hessian form: ax³ + y³ + 1 = dxy the twisted Edwards form: ax² + y² = 1 + dx²y² (used in EdDSA) the twisted Jacobi intersection form: bs² + c²