The Simplest Rational Right Triangle with Area 157 |
The Congruent Number Problem[Up] |
For any positive integer n, let E_{n} denote the elliptic curve defined by the equation y^{2} = x^{3} - n^{2}x. Then n is a congruent number if and only if E_{n} has infinitely many solutions. The curves E_{n} are quadratic twists of the elliptic curve y^{2} = x^{3} - x, which is isogenous to the modular curve X_{0}(32).