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'''Definition.''' Let <math>k</math> be a field in which <math>2 \neq 0</math>, and let <math>a,d \in k\setminus\{0\}</math> with <math>a\neq d</math>. Then the twisted Edwards curve <math>E_{E,a,d}</math> is given by <math>ax^2+y^2=1+dx^2y^2.</math> An Edwards curve is a twisted Edwards curve in which <math>a=1</math>.
There are five known ways to build a set of
The set of affine points is given by:
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