Weierstrass equations are a specific form of equations used to describe elliptic curves, which are important in number theory and algebraic geometry. They are typically written in the form y^2 = x^3 + ax + b , where a and b are constants. These equations help in studying the properties of elliptic curves, including their points and group structure. These equations are named after the mathematician Karl Weierstrass, who contributed significantly to the theory of complex functions and elliptic functions. Weierstrass equations play a crucial role in various applications, including cryptography and the proof of Fermat's Last Theorem.