I agree. I just tried substituting in a bunch of those points and none solved that equation. I don't see, for example, how the point at (12,56) fits that equation at all, since it computes to 56^2 = 12^3 - 12, or 3136 = 1728 - 12, or 3136 = 1716. That isn't even remotely close, so it's not me just slightly misreading the points.
The author omitted the mod n, where n = 71 in this case. So 3136 mod 71 = 1716 mod 71 = 12.
Oh of course! Thank you, that makes a lot more sense.