A curve X over Q is modular if it is dominated by X₁(N) for some N; if in addition the image of its jacobian in J₁(N) is contained in the new subvariety of J₁(N), then X is called a new modular curve.

Many complicated advances in research mathematics are spurred by a desire to understand some of the simplest questions about numbers. How are prime numbers distributed in the integers? Are there ...