In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form y² = x³ + ax + b. that is non-singular; that is, it has no cusps or self-intersections. Elliptic curves are especially important in number theory, and constitute a major area of current research; for example, they were used in the proof, by Andrew Wiles, of Fermat's Last Theorem. They also find applications in elliptic curve cryptography (ECC) and integer factorization. An elliptic curve is not an ellipse, Not to be confused with Ellipse. Topologically, a complex elliptic curve is a torus.
Formula:
y² = x³ + ax + b
where,y = Y coordinate
x = X coordinate
a = Linear coefficient
b = Free term