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How to get equation from given three points(with doubling) on twisted edwards curve over finite field?

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I have given three points $ P $, $ Q $, $ R $ on Twisted Edwards Curve over prime finite field $ \mathbb{Z}_p $. $$ ax^2 + by^2 = dx^2y^2 + 1 $$ I know about given points that point $ Q $ is doubling of point $ P $ and $ R $ is doubling of $ Q $. But I don't know the coefficient of curve's formula $ a $, $ b $, $ d $ and $ p $

How can I recover the coefficient of curve and $ p $ from these three points?

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