Exact computational search in the full 2-torsion/3-torsion family with p=-31, q=52; A=(3q-p)(p+q)^3=1731807, B=-(p+3q)(p-q)^3=71473375. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.
Natanael Wildner Fraga ·