Conformal geometry examines transformations that preserve angles, revealing deep interrelations between geometry and analysis. When combined with nonlinear elliptic equations—which are characterised ...

We construct a family of Diophantine triples {c₁(t), c₂(t), c₃(t)} such that the elliptic curve over Q(t) induced by this triple, i.e.: y² = (c₁(t) x + 1)(c₂(t) x + 1((c₃(t) x + 1) has torsion group ...

We present a method for constructing optimized equations for the modular curve X 1 (N) using a local search algorithm on a suitably defined graph of birationally equivalent plane curves. We then apply ...