The $j$-invariant for elliptic curves has a $1728$ in it. According to Hartshorne, this is supposedly for characteristic-$2$ and $3$ reasons, despite appearances to the contrary.
Indeed, it is unfathomable why it would help in char $2$ and $3$ when it would vanish.
For that matter, the functions $g_2$, $g_3$ and $\Delta$ too have these constants. Is there a ``good reason'' why these exist, other than historical reasons? And why are they kept on when we pass to abstract algebraic geometry, when $1728$ only seems to do harm?