The elliptic curve $y^2=x^3+3x+4$ has points O,(-1,0) and (0,2). Find five more points with rational coordinates.
The answer to this example gives: (0,-2) (5,-12) (5,12) (71/25,744/125) and (71/25,-744/125)
It seems to me that by changing the y coordinates sign you can automatically get another point, is this true?
Also I known how to calculate points P + Q, but in this case I don't see the mod explicitly expressed, do I have to solve for this?
Also is there a way to know how many points exist? Is it infinite or not?