A special cubic curve

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How can I transfer following cubic curve to a Weierstrass normal form? $$2x^2y+4xy^2+2y^3-2axy-ay^2+a=0,$$ where $a$ is a fixed rational number.

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With difficulty, or with Maple (which has this built in). The algorithm is described in this very nice (but nontrivial) paper by Mark van Hoeij.