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Finding Gaussian integer points on elliptic curves

How can I find all points whose coordinates are Gaussian integers? I know that finding all integer points for curves over rationals can be done by: E.S_integral_points([], both_signs=True) or E.integral_points(both_signs=True)

But these do not work with curve defined over "i"-extension of rationals.

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Finding Gaussian integer points on elliptic curves

How can I find all points whose coordinates are Gaussian integers? I know that finding all integer points for curves over rationals can be done by: E.S_integral_points([], both_signs=True) or E.integral_points(both_signs=True)

But these do not work with curve defined over "i"-extension of rationals.