Addition of Points on an Elliptic Curve over the Reals

curve coefficients

a

b

point positions

P

Q

labels

force Q = P

curve:

2

y

=

3

x

+ -

29

10

x+4

P≈ {0.943373,1.45044}

Q≈ {-1.80663,-1.82827}

P + Q ≈ {2.28473,-3.04969}

An elliptic curve over the reals forms a group under an addition law defined by line intersection and reflection. The controls allow for various elliptic curves and various points on those curves. The elliptic curve sum of the two points and the relevant lines are shown.