Specialization at (u,v)=(7,3) of the family in Yasutsugu Fujita and Nobuhiro Terai, On the Rank of the Elliptic Curve y^2 = x^3 - n*x (2012), Theorem 3.3: https://www.m-hikari.com/ija/ija-2012/ija-17-20-2012/teraiIJA17-20-2012.pdf . Here n=u^8+6*u^4*v^4+25*v^8=7095712 and the source equation is y^2=x^3-n*x. The three source sections seeded my point search, followed by the minimal-model change [u,r,s,t]=[4,0,0,0]. PARI/GP returned rank bounds [5,5]. All five listed rational points were checked exactly on the displayed global minimal model and independently certified. The rational torsion subgroup is Z/2Z.
Commentary
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