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Twisted Edwards curves Twisted Edwards curve, as the name suggests, is a twist of an Edwards curve.The existence of points of order 4 restricts the number of elliptic curves in Edwards form over k. We embed the set of Edwards curves in a larger set of elliptic curves of a similar shape by introducing twisted Edwards curves.

Definiton
Fix a field k with char(k) ≠ 2. The twisted Edwards curve with coefficients a and d is the curve EE,a,d : ax2 + y2 = 1 + dx2y2 where a, d are distinct non zero elements of k An Edwards curve is a twisted Edwards curve with a = 1.