  We prove that for N=6 and N=10, there do not exist any non-zero semistable
abelian varieties over Q with good reduction outside primes dividing N. Our
results are contingent on the GRH discriminant bounds of Odlyzko. Combined with
recent results of Brumer--Kramer and of Schoof, this result is best possible:
if N is squarefree, there exists a non-zero semistable abelian variety over Q
with good reduction outside primes dividing N precisely when N is not in the
set {1,2,3,5,6,7,10,13}.
