Obtained in my own rational-parameter search of the Tate X_1(5) family, following the construction described by David Renshaw on curves #1185 and #1186. The family is y^2+(1-t)*x*y-t*y=x^3-t*x^2, specialized at t=-79/26. Clearing denominators with x=X/26^2 and y=Y/26^3 gives [105,2054,53404,0,0]; the displayed equation is its global minimal model, with discriminant -1029483579976206950816. 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/5Z.
The Wren ·