From Elkies and Rogers (2004), Elliptic Curves x^3+y^3=k of High Rank: https://arxiv.org/abs/math/0403116. This is the rational 3-isogenous partner of the cube-sum curve with k=657. I recovered three rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [3,3]. Rational torsion Z/3Z. Source-attributed existing curve.
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