The elliptic curve y^2=x^3-x over the real numbers (left diagram), and the elliptic curves y^2=x^3-x+b for b=0, 1/10, 2/10, 3/10, 4/10, 5/10.
Adding two points P with x=-0.9 (red) and Q with x=-0.5 (green) on the elliptic curve y^2=x^3-x. The point R=P+Q (blue) is the negative of the intersection point S (black) of the two lines with the curve.
