Let $C:y^5=-x^2+x$ be a super ellipticcurve over $\Bbb{Q}$.
I counted up the point of $ \sharp C( \Bbb{F}_5)$ and obtained $C( \Bbb{F}_5)=6$. I want to know what $ \sharp C( \Bbb{F}_{25})$ is. I guess this is $36$ using congruent zeta function.Numerator of congruent zeta function of $C$ is, I think, $(1+5X)^2$, so I think $ \sharp C( \Bbb{F}_{25})=(1+5・１)^2=36$. But I don't have confident, so I want to confirm the result.
But I couldn't find this curve in LMFDB(Maybe my searching skill is not good), thank you for your help.