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 = 12510 gives the global minimal model Y^2 = X^3 - 1449075.
The explicit map is u = (A + 6Y)/(6X) and v = (A - 6Y)/(6X), with A = 12510. The three submitted points correspond to (u,v) = (23,7), (26831/1199,13099/1199), and (3655661/168142,2197699/168142).
All three points were checked exactly and are independent. Matching rank bounds [3,3] establish rank exactly 3, with trivial rational torsion and conductor 469500300.
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