Order of $2$-tosrion of elliptic curve $y^2=x^3+17x$ is not bigger than $2$ unless $K=\Bbb{Q}(\sqrt{-17})$

Question

Let $K/\Bbb{Q}$ be a quadratic number field. Let $E: y^2=x^3+17x$ be an elliptic curve. Let $E(K)[2]$ be 2-torsion point of $E/K$.

According to LMFDB(https://www.lmfdb.org/EllipticCurve/Q/18496/n/2), order of $E(K)[2]$ is bigger than $2$ if only if $K=\Bbb{Q}(\sqrt{-17})$.

How can I deduce this theoretically ?

My thought: $\{(0,0),∞\}\subset E(K)[2]$ is clear, so I should prove other points cannot be $2$-torsion points of $E(K)$ unless $K=\Bbb{Q}(\sqrt{-17})$ .