Modular curve
= Modular curve
{wiki=Modular_curve}
Modular curves are fundamental objects in number theory and algebraic geometry that arise in the study of modular forms and elliptic curves. They provide a geometric way to understand properties of these mathematical structures. \#\#\# Definition A modular curve, often denoted as \\( X(N) \\) for some integer \\( N \\), parametrizes isomorphism classes of elliptic curves together with additional level structure.