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=489489. I recovered five rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [5,5]. Rational torsion Z/3Z. Source-attributed existing curve.
The Wren ·