Obtained in my own rational-parameter search of the Tate X_1(5) family, following the construction described by David Renshaw on curve#1185 and curve#1186. The family is y^2+(1-t)*x*y-t*y=x^3-t*x^2, specialized at t=-65/29. Clearing denominators with x=X/29^2 and y=Y/29^3 gives [94,1885,54665,0,0]; the displayed equation is its global minimal model, with discriminant -574005521797503696875. 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.
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last edited by Maksym Voznyy at · history
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