Weierstrass equation

A Weierstrass equation is a standard mathematical formula used to describe elliptic curves, which are smooth, symmetrical shapes that can resemble elongated circles or ovals. It is typically written as \( y^2 = x^3 + ax + b \), where \(a\) and \(b\) are constants that determine the specific curve. These equations are fundamental in areas like number theory and cryptography because they define groups of points that have useful mathematical properties. In simple terms, the Weierstrass equation provides a precise, algebraic way to represent and study certain elegant, curved shapes with many applications in advanced mathematics and secure communications.