y^2=x^3+a*x+bAffine addition formulas: (x1,y1)+(x2,y2)=(x3,y3) where
x3 = (y2-y1)^2/(x2-x1)^2-x1-x2 y3 = (2*x1+x2)*(y2-y1)/(x2-x1)-(y2-y1)^3/(x2-x1)^3-y1Affine doubling formulas: 2(x1,y1)=(x3,y3) where
x3 = (3*x1^2+a)^2/(2*y1)^2-x1-x1 y3 = (2*x1+x1)*(3*x1^2+a)/(2*y1)-(3*x1^2+a)^3/(2*y1)^3-y1Affine negation formulas: -(x1,y1)=(x1,-y1).
The neutral element of the curve is the unique point at infinity, namely (0:1:0) in projective coordinates.
a=0and represent x y as X Y Z satisfying the following equations:
x=X/Z^2 y=Y/Z^3
Jacobian coordinates with a4=-3 [more information] make the additional assumptions
a=-3and represent x y as X Y Z satisfying the following equations:
x=X/Z^2 y=Y/Z^3
Jacobian coordinates [more information] represent x y as X Y Z satisfying the following equations:
x=X/Z^2 y=Y/Z^3
Modified Jacobian coordinates [more information] represent x y as X Y Z T satisfying the following equations:
x=X/Z^2 y=Y/Z^3 T=a*Z^4
Projective coordinates with a4=-1 [more information] make the additional assumptions
a=-1and represent x y as X Y Z satisfying the following equations:
x=X/Z y=Y/Z
Projective coordinates with a4=-3 [more information] make the additional assumptions
a=-3and represent x y as X Y Z satisfying the following equations:
x=X/Z y=Y/Z
Projective coordinates [more information] represent x y as X Y Z satisfying the following equations:
x=X/Z y=Y/Z
W12 coordinates with a6=0 [more information] make the additional assumptions
b=0and represent x y as X Y Z satisfying the following equations:
x=X/Z
y=Y/Z^2
XYZZ coordinates with a4=-3 [more information] make the additional assumptions
a=-3and represent x y as X Y ZZ ZZZ satisfying the following equations:
x=X/ZZ y=Y/ZZZ ZZ^3=ZZZ^2
XYZZ coordinates [more information] represent x y as X Y ZZ ZZZ satisfying the following equations:
x=X/ZZ y=Y/ZZZ ZZ^3=ZZZ^2
XZ coordinates [more information] represent x y as X Z satisfying the following equations:
x=X/Z