The isogenies of type $A_n$ are indexed by the subgroups of $\mathbb{Z} / (n+1) \mathbb{Z}$, i.e. by the positive divisors of $n+1$.  If $a$ is a positive integer and $a \mid (n+1)$, then the cocharacter lattice corresponding to the isogeny is given by $\langle Q^{\vee}, \epsilon_a \rangle$, where $Q^{\vee}$ is the coroot lattice and $$\epsilon_a = \frac{1}{n} [(n-a)(e_1 + e_2 + ... + e_a) - a(e_{a+1} + e_{a+2} + ... + e_{n+1}].$$

I would like a "nice" basis for this cocharacter lattice...nice for computational purposes (I am being vague for now on what this means).  For example, if the group is simply connected, then (I would say that) the set of simple coroots form a nice basis.  If the group is adjoint, then (I would say that) the set of fundamental coweights form a nice basis.

But what if the group is neither simply connected nor adjoint?  Is there a standard/nice basis that people use when computing with these isogenies?  Or is there a basis that you think seems "nice"?