An explicit Gross-Zagier formula related to the Sylvester Conjecture

Yueke Hu, Jie Shu, Hongbo Yin

Let $p\equiv 4,7\mathrm{mod}9$ be a rational prime number such that $3\mathrm{mod}p$ is not a cubic residue. In this paper we prove the 3-part of the product of the full BSD conjectures for $E_p…