# Integer solutions in elliptic curves

If $$E : y^2 = x^3 + ax^2 + bx + c$$ is an elliptic curve defined over the Rational Field, there exists at least $2$ points in $E$ with integer coordinates? Any theorem state this or something in the same way?

• No, there can be none (e.g. $y^2=x^3+6$) and there can be exactly one (e.g. $y^2=x^3+27$). – Wojowu Mar 3 '18 at 21:51