Obtained in my own bounded discriminant-first search of the integral Tate X_1(3) family, following the method described by jesper-petersen on curve #3759. The specialization a=256, b=-1 in y^2+a*x*y+b*y=x^3 gives y^2+256*x*y-y=x^3, with discriminant -16777243. The displayed equation is its global minimal model. All three listed rational points were checked exactly and returned as an independent set, with rank bounds [3,3]. The rational torsion subgroup is Z/3Z.
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