Found by a rational-parameter search of the Kubert-Tate family for torsion 6, at t=1/6916. In y^2+(1-c)xy-by=x^3-bx^2 the parameters are defined by c=t; b=t*(t+1); converted to the global minimal model.
Torsion Z/6, rank exactly 4 (GRH): the four points are independent by
the mod-2 Kummer-map test and the 2-Selmer rank is 4.
Conductor 33127795610 = 2 * 5 * 7 * 13 * 19 * 277 * 6917,
minimal discriminant 2^4 * 5^2 * 7^2 * 13^2 * 19^2 * 277 * 6917^3 = 109618302873088494976400.
Lewis Combes ·