Hyperbola

Let \(\mathrm{H}_{\mathrm{n}}: \frac{x^{2}}{1+n}-\frac{y^{2}}{3+n}=1, n \in N\). Let \(\mathrm{k}\) be the smallest even value of \(\mathrm{n}\) such that the eccentricity of \(\mathrm{H}_{\mathrm{k}}\) is a rational number. If \(l\) is the length of the latus rectum of \(\mathrm{H}_{\mathrm{k}}\), then \(21 l\) is equal to ____________.