on ranks of twists of elliptic curves and power-f ree values of binary forms
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on ranks of twists of elliptic curves and power-f ree values of binary forms
denote a quadratic twist of E given by the equation d y2 = x3 + ax + b. Let r(d) denote the rank of Ed. Note that if (2'1 and d2 are non-zero integers, then E d! is ...