All of the elliptic curves we work with in this chapter are elliptic curves mod However, it is helpful use the graphs of elliptic curves with real numbers in order to visualize what is happening with the addition law, for example, even though such pictures do not exist mod
Let’s graph the elliptic curve We’ll specify that and and make sure that
y are cleared of previous values.
> x:=’x’;y:=’y’;implicitplot(2=x*(x-1)*(x+1), x=-1..3,y=-5..5)
Add the points (1, 3) and (3, 5) on the elliptic curve