Central $L$ values of congruent number elliptic curves

Xuejun Guo, Dongxi Ye, Hongbo Yin

Let $E_n$ be the congruent number elliptic curve $y^2=x^3-n^{2}x$, where $n$ is square-free and not divisible by primes $p\equiv 3(\mathrm{mod}4)$. In this paper, we prove that $L(E_n,1)$ ca…