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11. Points on Elliptic Curves over Finite Fields


    1. Add remark

      Problem 11.1.

      [Colin Ingalls] Is there an elliptic curve over $\mathbb{Z}$ such that, for every prime $p$ (or just infinitely many primes $p$), it has exactly $p$ points over $\mathbb{F}_p$?
          Matt Satriano found a reference saying that this is false.

          Cite this as: AimPL: Noncommutative surfaces and Artin's conjecture, available at http://aimpl.org/ncsurfaceartin.