= Solution
For the <Weierstrass equation of an elliptic curve> in this part, $a_1=a_2=a_6=0$, $a_3=1$, $a_4=-1$. Hence
$$
b_2=0,\qquad b_4=-2,\qquad b_6=1,\qquad c_4=48,\qquad c_6=-216.
$$
The <elliptic-curve discriminant> is therefore
$$
\boxed{\Delta=\frac{48^3-216^2}{1728}=37.}
$$
Every <prime> other than $37$ has unit discriminant, so this integral equation gives <good reduction>. At $37$ the <valuation> is one. An <Admissible change of Weierstrass coordinates> changes discriminant <valuations> by a multiple of twelve; consequently no integral model can lower this value to zero. Thus the equation is minimal there and the reduction is genuinely bad, rather than an artifact of a nonminimal model. Explicitly $(5,18)$ is singular on the reduced affine cubic: both partial derivatives vanish there. The set of <bad reduction> primes is
$$
\boxed{\{37\}.}
$$
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