A family of elliptic curves of rank ≥ 5 over Q(m)
A family of elliptic curves of rank ≥ 5 over Q(m)
We construct a subfamily of elliptic curves E(r, s) : (y -s)(y + s) = x(x -r)(x + r) with r = 2(m 4 -2m 3 + 2m 2 + 2m + 1), s = 2(m 2 -2m -1)(m 2 + 1) 2 , and show that its rank is …