Most of the normalisation of modular symbols was introduced by me so let me comment.
There are currently two ways of computing modular symbols, one using eclib and the other the native sage implementation. Both are only correct up to a scaling factor. That is because their main use was as generators for some Q-vector space to produce modular forms etc. Instead if we start with an elliptic curve then there is a unique normalisation such that the modular symbol [0] takes the value L(E,1)/Omega+ where Omega+ is the least positive real period. In particular this depends on the curve and not just on the isogeny class (i.e. the modular form). So currently sage or eclib produce some Q-valued symbol and then we use the L-value to find the correct rational scaling factor. However if this L-value (and [0]) is zero, then we can't do it like that. Instead we can use a quadratic twist to get a non-zero L-value. For the curves where the warning message comes, sage was not able to find a good quadratic twist. This could be improved. However there is a ticket waiting that will implement a thrid way of computing the modular symbols (much faster when asked only a few of them): https://trac.sagemath.org/ticket/21046 . Once this is in, I will change the normalisation to used these numerical symbols to get the right scaling factor also for the other two implementations. Then this warning will disappear. Chris On Wednesday, 9 November 2016 00:25:33 UTC, francisco wrote: > > Hello, > > I have been computing modular symbols for distinct curves on the Cremona > data base. > But, in a few curves, I recived a WARNING messages like this: > > Warning : Could not normalize the modular symbols, maybe all further > results will be multiplied by -1, 2 or -2. > > Why sage does not give the exact normalization? Is there a theoretical > reason? > How sage normalize modular symbols? > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
