On page 22 it shows an elliptic curve over F17.
I have added the orange lines and labels.
Do the orange lines illustrate that a line through points at P(2,10) and Q(5,9) also intersects the "curve" at -R(12,1)?
i.e. Does the finite field version graphically match an elliptic curve over real numbers, with the provisos that the finite field curve is discontinuous and that lines wrap?
Or am I hopelessly confused about elliptic curves on finite fields (as I expect).
P.S. If this is an accurate graphical representation, how do I illustrate tangents to the discontinuous curve?
P.P.S. There are multiple lines which contain three points. X, Y and -Z, in purple, are another (below).