On the high rank $\pi /3$ and $2\pi /3$-congruent number elliptic curves

Ali S. Janfada, Sajad Salami, andrej Dujella +1

Consider the elliptic curves given by $E_{n,\theta }:y^2=x^3+2sn{x}^2-(r^2-s^2)n^{2}x$ where $0<\theta <\pi$, $\cos (\theta )=s/r$ is rational with $0\le |s|<r$ and $\gcd (r,s)=1$. These e…