Modular elliptic curves

Modular elliptic curves are special types of curves studied in number theory that have deep connections to the properties of modular forms—complex functions with symmetrical patterns. These curves can be described with algebraic equations and display remarkable symmetry and structure. Their significance lies in their role within the proof of famous mathematical problems, like Fermat's Last Theorem, by linking solutions to equations with modular forms. Essentially, modular elliptic curves serve as a bridge connecting the geometry of equations to the analytic world of functions, revealing profound insights into number properties and symmetries.