All solutions to Thomas' family of Thue equations over imaginary quadratic number fields

We completely solve the family of relative Thue equations x 3 (t 1)x 2 y (t + 2)xy 2 y 3 = µ, where the parameter t, the root of unity µ and the solutions x and y are integers in the same imaginary quadratic number field. This is achieved using the hypergeometric method for |t| � 53 and Baker's method combined with a computer search using continued fractions for the remaining values of t.

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