  Reaching for a better understanding of turbulence, a line of investigation
was followed, its main presupposition being that each scale dependent state, in
a general renormalization flow, is a state that can be modeled using a class of
ninth degree polynomials. These polynomials are deduced from the Weierstrass
models of a certain kind of elliptic curves. As the consequences of this
presupposition unfolded, leading to the numerical study of a few samples of
elliptic curves, the L functions associated with these later were considered.
Their bifurcation diagrams were observed and their escape rates were
determined. The consistency of such an approach was put to a statistical test,
measuring the rank correlation between escape rates and values taken by these L
functions on the point z=1+0i. In the most significant case, the rank
correlation coefficient found, r_s, was about r_s=-0.78, with an associated
p-value of an order of magnitude close to the (-69) power of 10.
