  While there has been considerable interest in the problem of finding elliptic
curves of high rank over $\mathbb{Q}$, very few parametrized families of
elliptic curves of generic rank $\geq 8$ have been published. In this paper we
use solutions of certain symmetric diophantine systems to construct several
parametrized families of elliptic curves with their generic ranks ranging from
at least 8 to at least 12. Specific numerical values of the parameters yield
elliptic curves with quite large coefficients and we could therefore determine
the precise rank only in a few cases where the rank of the elliptic curve $\leq
13$. It is, however, expected that the parametrized families of elliptic curves
obtained in this paper would yield examples of elliptic curves with much higher
rank.
