I would like to find a upper bound of principal polarization of abelian variety in the following stiution:

Suppose $A$ is an abelian variety over a $char=0$ algebraically closed field. And for any two principal polarization $\lambda_1$, $\lambda_2$:$A \to A^t$, we we say they are eqivalent if and only if there exsits an isomorphism $\sigma\in Aut(A)$ such that $\lambda_1=\sigma^t \circ\lambda_2\circ\sigma$.

Now, let $T$ be the collection of the principal polarization of $A$, is there any upper bound (which is just relative to the dimension $g$) of the cardnarity of $T$/~?