On the Existence of Elliptic Curves of Mordell–Weil Rank 6 with Four Parameters Original Research Article

We construct an elliptic curve defined overQwith Mordell–Weil rank greater-or-equal, slanted6 as a generic twist by a certain quadratic extension. Moreover, since they have four independent parameters, they give us rather a large supply of elliptic curves defined overQwith rank greater-or-equal, slanted6. As an application, we find infinitely many pairs (a, b) of rational numbers such that the elliptic curveby2=x3+ax2+ax+1 is of Mordell–Weil rank greater-or-equal, slanted6.