8
$\begingroup$

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.

$\endgroup$
13
$\begingroup$

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.

$\endgroup$
  • $\begingroup$ Thank you, Carlo! $\endgroup$ – ABarrios Aug 10 at 14:21

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.