Elliptic curve
In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined over a field K and describes points in K2, the Cartesian product of K with itself. If the field's characteristic is different from 2 and 3, then the curve can be described as a plane algebraic curve which consists of solutions (x, y) for: y 2 = x 3 + a x + b {\displaystyle y^{2}=x^{3}+ax+b} for some coefficients a and b in K. The curve is required to be non-singular, which means that the curve has no cusps or self-intersections.