  Let $M$ be the moduli space of rank 3 stable bundles with fixed determinant
of degree 1 on a smooth projective curve of genus $g\geq 2$. When $C$ is
generic, we show that any essential elliptic curve on $M$ has degree (respect
to anti-canonical divisor $-K_{M}$) at least 6, and we give a complete
classification for elliptic curves of degree 6, which is not in conformity with
Sun's Conjecture. Moreover, if $g>12$, we show that any elliptic curve passing
through the generic point of $M$ has degree at least 18.
