Abstract
Building on Finotti in (Acta Arith 139(3):265–273, 2009), we give an elementary proof for the well known result that there exactly \(\lceil (p-1)/4 \rceil -\lfloor (p-1)/6 \rfloor\) supersingular elliptic curves in characteristic p. We use a related polynomial instead of the supersingular polynomial itself to simplify the proof and this idea might be helpful to prove other results related to the supersingular polynomial.
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Communicated by Claudio Gorodski.
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Finotti, L.R.A. An elementary proof for the number of supersingular elliptic curves. São Paulo J. Math. Sci. 14, 531–538 (2020). https://doi.org/10.1007/s40863-020-00170-8
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DOI: https://doi.org/10.1007/s40863-020-00170-8