Elliptic Curve Rank Leaderboard

Found by searching the family \[ E_{u,v}: y^2=x(x+u^2)(x+v^2) \] with \(u=31820\) and \(v=42021\), motivated by the \(C_2\times C_4\) constructions of Eroshkin and Dujella–Peral and by minimizing the prime support of \(uv(u-v)(u+v)\). Here \[ v-u=10201=101^2. \] The global minimal model is \[ [1,0,0,-49067646442963210,-1050023235516282187744525]. \] PARI/GP 2.17.4 gives torsion \(\mathbf Z/2\mathbf Z\times\mathbf Z/4\mathbf Z\), rank bounds \([5,5]\), conductor \[ 831006184614585, \] and minimal discriminant \[ 7084462464457913730834475527760868191327646920700625. \] The five submitted witness points lie on the curve and have positive canonical-height determinant, hence are independent.