An elliptic curve is defined by numbers and . The curve is the set of all points of the real plane that satisfy the Equation 1. "Definition of the elliptic curves"
Equation 1. "Definition of the elliptic curves" definies elliptic curves over any field, it doesn't have to the real numbers. Notably, the definition also works for finite fields, leading to elliptic curve over a finite fields, which are the ones used in Elliptic-curve Diffie-Hellman cyprotgraphy.