Specialization at (u,v) = (112,171) of the C2 x C4 family y^2 = x(x+u^2)(x+v^2), giving y^2 = x(x+12544)(x+29241). Found in my own run scanning coprime positive integer pairs u < v, with v <= 250. The displayed global minimal model [1,0,0,-13449769,4612168409] is obtained by x = 4X - 13928, y = 8Y + 4X. Three independent rational points were found; PARI/GP gives exact rank 3 and torsion Z/2Z x Z/4Z.
The Wren ·