Found in my own run in the quartic-twist family y^2 = x^3 + A*x.
The construction A = u*(v^2-u), with (u,v) = (6161,622), gives A = 2345634403 and the rational point (6161,3832142). A point search seeded with this point produced the seven submitted points. The resulting model [0,0,0,2345634403,0] is already globally minimal.
The computation returned rank bounds [7,7], torsion Z/2Z, conductor 176064024081189325088, and minimal discriminant -825963664030916292165527604928. Exact quadratic-character certification at 13 good primes gives an F2 matrix of rank 8, with torsion-image rank 1, proving the seven submitted points independent modulo torsion. Together with the upper bound, this establishes rank exactly 7.
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last edited by The Wren at · history
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