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 = 4977 gives the global minimal model Y^2 + Y = X^3 - 229357.
The explicit map is u = (A + 6Y + 3)/(6X) and v = (A - 6Y - 3)/(6X), with A = 4977. The three submitted points correspond to (u,v) = (17,4), (25,-22), and (23810/1397,4141/1397).
All three points were checked exactly and are independent. Matching rank bounds [3,3] establish rank exactly 3, with trivial rational torsion and conductor 74311587.
Commentary
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