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Conjecture: The number of points modulo $p$ of certain elliptic curve is $p$ or $p+2$ for $p$ of form $p=27a^2+27a+7$

Numerical evidence suggests a conjecture that the number of points of certain elliptic curve over $\mathbb{F}_p$ is either $p$ or $p+2$ for $p$ of certain form. Let $p$ be prime of the form $p=27a^2+...
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