= Solution
The <elliptic-curve discriminant> is $37$, so the <elliptic curve> has <good reduction> at both $2$ and $3$. At a prime $\ell$ of <good reduction>, the <reduction of torsion points on an elliptic curve> is injective on torsion of order prime to $\ell$. Here is the formal reason: the <kernel of reduction of an elliptic curve> is described by an integral <formal group law> on $\ell\mathbb Z_\ell$, and its multiplication series is $[n](t)=nt+O(t^2)$. If $\ell\nmid n$, the first term has strictly smaller <valuation> than every higher term for $t\ne0$. Thus this kernel has no nonidentity point killed by $n$.
Apply this to each prime-primary component of the rational <torsion subgroup>. A component at $2$ injects into $\widetilde E_3(\mathbb F_3)$, of order $7$, and is therefore trivial. A component at $3$ injects into $\widetilde E_2(\mathbb F_2)$, of order $5$, and is trivial. Every other prime-primary component injects into both groups, so its order divides $\gcd(5,7)=1$. This proves the <two-prime bound on rational elliptic torsion> in the present case:
$$
\boxed{E(\mathbb Q)_{\mathrm{tors}}=\{O\}.}
$$
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