Abstract: Complex abelian varieties are the algebraic version of compact, connected, commutative complex Lie groups. They are embeddable into projective spaces and have many types of invariants. For instance, their Mumford--Tate groups are reductive groups over Q which can be viewed as analytic invariants. When the complex abelian varieties are definable over number fields, one associates to them several arithmetic invariants which encode their good reductions at finite primes. An old conjecture of Morita pertains to the impact of the Morita--Tate groups on the mentioned arithmetic invariants. We report on a solution of this conjecture in a very general case.