id,summary,reporter,owner,description,type,status,priority,milestone,component,resolution,keywords,cc,merged,author,reviewer,upstream,work_issues,branch,commit,dependencies,stopgaps
12080,manin constant,wuthrich,cremona,"My definition of the Manin constant of an elliptic curve E/Q is the rational number c such that
phi(omega) = c * f dq/q
where
* phi is the modular parametrisation X_0(N) -> E of minimal degre
* omega is the Neron differential on E
* f is the normalised newform
* q is q=exp(2pi i tau) as usual
With this definition I get a different answer than sage. For instance for 11a2, I get 1 not 5.
Either one has to change the implementation or one has to add to the documentation the definition of what is computed.
The current implementation (from #5138 ) computes the minimal degree of an isogeny from E to the X_0-optimal curve E_0 and multiplies the manin constant of E_0 by this degree. Instead, with my definition, we have to multiply with the number c' where psi*(omega) = c' * omega_0 with psi the isogeny E_0 -> E of minimal degree and omega_0 the Neron differential of E_0. This c' is a divisor of the degree of psi, but on many occasions it is 1.
",defect,closed,major,sage-5.0,elliptic curves,fixed,"manin constant, isogeny",was,sage-5.0.beta12,Chris Wuthrich,William Stein,N/A,,,,,