Obtained in my bounded search using the divisor-square construction described by jesper-petersen on curves #1249, #3756 and #3757, following Thomas J. Kretschmer, Construction of Elliptic Curves with Large Rank, Mathematics of Computation 46 (1986), 627–635.
The search parameters were A = -232 and B = 12012 in y^2 = x^3 + A*x^2 + B*x. A divisor pair b1*b2 = B with b1 + A + b2 = s^2 supplies the point (b1,b1*s). Substituting x = X + 77 gives the displayed minimal model. The three listed independent rational points were checked exactly on this model, and the computed lower and upper rank bounds both equal 3. The rational torsion subgroup is Z/2Z × Z/2Z.
The Wren ·