Yep, there are vertical lines that intersect the curve at only two points. In that case there is a special "infinity" point (also known as zero). See page 21 in

Yep, there are vertical lines that intersect the curve at only two points. In that case there is a special "infinity" point (also known as zero). See page 21 in this presentation which I think explains it a little bit better: https://www.math.brown.edu/johsilve/Presentations/WyomingEllipticCurve.pdf https://www.math.brown.edu/johsilve/Presentations/WyomingEll...