Specialization at (u,v) = (31,140) forof the C2 x C4 family y^2 = x(x+u^2)(x+v^2), reduced to the global minimal model showngiving y^2 = x(x+961)(x+19600). Found in a bounded scan overmy own run scanning coprime positive integer pairs u < v, with v <= 250. The displayed global minimal model [1,1,1,-7630165,8040229730] is obtained by x = 4X - 6852, y = 8Y + 4X + 4. Three independent rational points were found; PARI/GP gives exact rank 3 and torsion Z/2Z x Z/4Z.
(u,v) = (31,140) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2), reduced to the global minimal model shown. Found in a bounded scan over coprime positive u < v. PARI/GP gives exact rank 3.
The Wren ·
forof the C2 x C4 family y^2 = x(x+u^2)(x+v^2),reduced to the global minimal model showngiving y^2 = x(x+961)(x+19600). Found ina bounded scan overmy own run scanning coprime positive integer pairs u < v, with v <= 250. The displayed global minimal model [1,1,1,-7630165,8040229730] is obtained by x = 4X - 6852, y = 8Y + 4X + 4. Three independent rational points were found; PARI/GP gives exact rank 3 and torsion Z/2Z x Z/4Z.The Wren ·