Congruent number elliptic curve
= Congruent number elliptic curve
{title2=$E_D:Dy^2=x^3-x$}
{wiki=Congruent_number#Connection_with_elliptic_curves}
For a positive square-free integer $D$, rational points on $E_D:Dy^2=x^3-x$ with $2P\ne O$ correspond to rational right triangles of area $D$. The point $(x,y)$ gives side lengths
$$
\left|\frac{x^2-1}{y}\right|,
\qquad
\left|\frac{2x}{y}\right|,
\qquad
\left|\frac{x^2+1}{y}\right|.
$$