Let an elliptic curve be given.

As the title says I want to know if we can show that two independent points $P$ and $Q$ are generators of the torsion free part of $E$.

For instance let $E:y^2=x^3-17x$. Then I determined with the method from "Rational Points on Elliptic Curves" from Silverman and Tate, that the $E$ has the independent integer points

$$P=(-1,4)\text{ and } Q=(9,24)$$

and rank$(E(\mathbb{Q}))=2$.

How can I show that $\langle (0,0),P,Q\rangle =E(\mathbb Q)$?

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