Question: If you Let p 2 (mod 3) be a prime, and let a number c F p . Prove that the elliptic curve C :

If you Let p 2 (mod 3) be a prime, and let a number c F_p. Prove that the elliptic curve C : y²= x³+ c satisfies #C(Fp) = p + 1.

(Hasse-Weil Theorem). If C is a non-singular curve, that cannot be reduced. And it has genus g defined over a finite field F_p, then the amount points on C with their coordinates in F_pis equal to p + 1 +e, where the "error term" e satisfies the inequality,

|e| 2g p

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