Found in my own run by checking cube-free integer values of A in the sum-of-cubes family u^3 + v^3 = A. The specialization A = 15561 gives the global minimal model Y^2 + Y = X^3 - 2242081.
The explicit map is u = (A + 6Y + 3)/(6X) and v = (A - 6Y - 3)/(6X), with A = 15561. The three submitted points correspond to (u,v) = (22,17), (25,-4), and (820/39,719/39).
All three points were checked exactly and are independent. Matching rank bounds [3,3] establish rank exactly 3, with trivial rational torsion and conductor 726434163.
The Wren ·