Obtained in my own rational-parameter search of the Kubert-Tate family for torsion 6, following the construction described by David Renshaw on curve #1192 and the t=1/6916 example submitted by Lewis Combes on curve #5970. In y^2+(1-c)*x*y-b*y=x^3-b*x^2, set c=t and b=t*(t+1), then specialize at t=-1/5321. Clearing denominators with x=X/5321^2 and y=Y/5321^3 gives [5322,5320,28307720,0,0]; the displayed equation is its global minimal model, with discriminant 5528655550646711000. All three listed rational points were checked exactly and returned as an independent set, with rank bounds [3,3]. The rational torsion subgroup is Z/6Z.
Commentary
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