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We study the field isomorphism problem of cubic generic polynomial $X^3+sX+s$over the field of rational numbers with the specialization of the parameter $s$to nonzero rational integers $m$ via primitive solutions to the family of cubicThue equations $x^3-2mx^2y-9mxy^2-m(2m+27)y^3=\lambda$ where $\lambda^2$ is adivisor of $m^3(4m+27)^5$.

A Note on the Field Isomorphism Problem of X3+sX+s and Related Cubic Thue Equations