Found by a conductor-oriented search in the standard Z/2Z x Z/4Z family
y^2 = x(x+u^2)(x+v^2), with (u,v) = (2278,69125).
The search used smooth-support / conductor filtering followed by Nagao scoring
and exact rank computation. PARI/GP 2.17.4 gives exact rank 6 and torsion
Z/2Z x Z/4Z.
jesper-petersen ·