Is Bhargava multidimensional matrices and elliptic curves methods applying also to finite fields?

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There are a bunch of papers of Bhargava et al. 1 and 2 where they use multidimensional matrices and hyperdetermimant to derive theorems about the average ranks of genus 1 or 2 curves over rational fields. Are these multidimensional matrices techniques also valid for elliptic curves over finite fields?