Historical mathematical exhibit
The Congruent Number Problem
A positive integer n is congruent when it is the area of a right triangle with rational side lengths.
The original X0(32) lookup and congruent-number CGI forms have been retired. One of them was explicitly unfinished in the archived page.
Elliptic-curve formulation
For a positive integer n, let En be y2 = x3 - n2x. Then n is congruent exactly when En has positive rank. These curves are quadratic twists of y2 = x3 - x, which is isogenous to X0(32).
The triangle of area 157 Talk slides (PostScript) Original StarOffice slides
