In this talk we will introduce some distributions that can be studied in large families of curves over finite fields. After giving a panorama of which families of curves have been considered, we introduce the family of biquadratic curves, i.e. quartic non-cyclic covers of the projective line $\mathbb{P}^{1}_{\mathbb{F}_{q}}$, and we state the results obtained in this case.
This is a joint work with Elisa Lorenzo and Giulio Meleleo.
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