  Given a rational elliptic curve $ E $ of analytic rank zero, its L-function
can be twisted by an even primitive Dirichlet character $ \chi $ of order $ q
$, and in many cases its associated central algebraic L-value $ \mathcal{L}(E,
\chi) $ is known to be integral. This paper derives some arithmetic
consequences from a congruence between $ \mathcal{L}(E, 1) $ and $
\mathcal{L}(E, \chi) $ arising from this integrality, with an emphasis on cubic
characters $ \chi $. These include $ q $-adic valuations of the denominator of
$ \mathcal{L}(E, 1) $, determination of $ \mathcal{L}(E, \chi) $ in terms of
Birch--Swinnerton-Dyer invariants, and asymptotic densities of $ \mathcal{L}(E,
\chi) $ modulo $ q $ by varying $ \chi $.
