Abstract
We construct an elliptic curve defined overQwith Mordell–Weil rank ⩾6 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 ⩾6. 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 ⩾6.
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