id	summary	reporter	owner	description	type	status	priority	milestone	component	resolution	keywords	cc	work_issues	upstream	reviewer	author	merged	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		N/A	William Stein	Chris Wuthrich	sage-5.0.beta12