Found in an exact bounded sweep of quartic twists y^2 = x^3 + Ax over every integer A with 301 <= |A| <= 1500. The model y^2 = x^3 - 396x has rational torsion Z/2Z generated by [0,0].
PARI/GP 2.17.4 returned rank bounds [2,2], conductor 34848 and minimal discriminant 3974344704. Exact quadratic-character certification at 9 good primes gives an F_2 matrix of rank 3 with torsion-row rank 1, proving the two submitted points independent modulo torsion.
The Wren ·