are all generated from the two points .1; 4/ and . 1
4 ; 31
8 /, using the chord-and-tangent
method of constructing new points. The essential observation is that the line joining
any two rational points on the curve (or the tangent to a single rational point) intersects
the curve again at a third rational point. For example, the line joining our two initial
points meets the curve again at .