# Max order of an isogeny class of rational elliptic curves is 8?

I am looking for a reference for the proof of the following question following Theorem 5 in Mazur's Rational Isogenies of Prime Degree.

Theorem 5 There is a constant $$C$$ such that every elliptic curve $$E_{/\mathbb{Q}}$$ is isogenous (over $$\mathbb{Q}$$) to at most $$C$$ (mutually nonisomorphic) elliptic curves.

"Can one take $$C=8$$?"

Has this question been settled? And if so, what is a reference to the proof of the result.

M. Kenku, On the number of $$\mathbf{Q}$$-isomorphism classes of elliptic curves in each $$\mathbf{Q}$$-isogeny class, J. Number Theory 15, 199 (1982):
It is shown that there are at most eight $$\mathbf{Q}$$-isomorphism classes of elliptic curves in each $$\mathbf{Q}$$-isogeny class.