The Weierstrass Elliptic Function is a complex function that arises in the study of elliptic curves and complex analysis. It is defined using a lattice in the complex plane, which allows it to exhibit periodic properties. This function is denoted as ℘(z) and is characterized by its double periodicity, meaning it is periodic in two directions. The Weierstrass Elliptic Function plays a crucial role in various areas of mathematics, including number theory and algebraic geometry. It can be used to construct elliptic curves, which are important in cryptography and the study of Diophantine equations. Its properties also connect to Jacobi Elliptic Functions and modular forms.