How do you compute the number of points of an elliptic curve over a finite field?
Given an elliptic curve defined over
,
Sage can compute its set of
-rational points
sage: E = EllipticCurve(GF(5),[0, -1, 1, -10, -20]) sage: E Elliptic Curve defined by y^2 + y = x^3 + 4*x^2 over Finite Field of size 5 sage: E.points() [(0 : 0 : 1), (0 : 1 : 0), (0 : 4 : 1), (1 : 0 : 1), (1 : 4 : 1)] sage: E.cardinality() 5 sage: G = E.abelian_group() sage: G # random choice of generator (Multiplicative Abelian Group isomorphic to C5, ((1 : 0 : 1),)) sage: G[0].permutation_group() Permutation Group with generators [(1,2,3,4,5)]
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