Abstract
We study the Jacobians of the genus 3 Picard and Fermat curves with respect to the problem of maximizing the minimum non-zero norm. We use criteria for symplectic lattices related to the criteria of perfect and eutactic for classical lattices. We show that the Picard curve is a local maximum, but the Fermat curve is not.
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Quine, J.R., Zhang, P.L. Extremal symplectic lattices. Israel J. Math. 108, 237–251 (1998). https://doi.org/10.1007/BF02783050
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DOI: https://doi.org/10.1007/BF02783050