$S$ denotes the set of rational points of any curve in the plane.
What is more amazing between a) and b)?
a) $S$ is dense in the curve $y^2=x^3-2^4\cdot3^3\cdot7^2$
b) $S=\emptyset$ in the curve $y^2=x^3-2^4\cdot3^3\cdot5^2$
N.B.- Both, a) and b) are true.
