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Let $ E_1: y^{2}=x^{3}-D_1 x $ be elliptic curves over the Gaussian field $K=\\Q(\\sqrt{-1}), $ with $ D_1 =\\pi_{1} ... \\pi_{n} $ or $ D_1 =\\pi_{1} ^{2}... \\pi_{r} ^{2} \\pi_{r+1} ... \\pi_{n}$, where $\\pi_{1}, ..., \\pi_{n}$ are distinct primes in $K$. 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