Abstract

We study the field isomorphism problem of cubic generic polynomial X3+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 cubic Thue equations x3−2mx2y−9mxy2−m(2m+27)y3=λ where λ2 is a divisor of m3(4m+27)5.

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