Re: Support for elliptic curves over number fields

[John Cremona <john.cremona@gmail.com>]

On 30 Jul 2016 7:07 p.m., "John Cremona" <john.cremona@gmail.com> wrote:
>
> Thanks Bill -- I will change the nfinit line and will report the
> L-function issue to the appropriate LMFDB-devs.

These are now issues 1895 and 1896 on github/LMFDB

>
> John
>
> On 28 July 2016 at 11:04, Bill Allombert
> <Bill.Allombert@math.u-bordeaux.fr> wrote:
> > On Thu, Jul 28, 2016 at 12:40:12AM +0200, Bill Allombert wrote:
> >> On Mon, Jul 25, 2016 at 11:05:06AM +0200, Bill Allombert wrote:
> >> > Could you change the way the field is defined ?
> >> >
> >> > Instead of
> >> >   K = nfinit(x^3 - x^2 - 3*x + 1); a=x
> >> >
> >> >   K = nfinit(a^3 - a^2 - 3*a + 1);
> >> > would be better
> >> >
> >> > (Also LMFDB gives the L-function of E as
> >> > L(s,f)  = 1− 4^-s − 0.447·5^-s − 0.832·13^-s + 16^-s + 0.485·17^-s +...
> >> > but I do not think this is correct: it should be
> >> > L(s,f)  = 1− 0.447·5^-s − 0.832·13^-s + 0.485·17^-s +...
> >> > The true L-function of E have a trivial Euler factor at 2.
> >> > I assume this is an instance of two L-functions differing by
> >> > a single Euler factor at 2, which can happen in motivic weight 1).
> >>
> >> No actually the Euler factor at 89 is also different, and maybe I did
> >> something wrong, but the LMFDB L-function does not satisfy the stated
> >> functional equation.
> >>
> >> I used
> >> L2=lfuncreate([H,0,[1/2,1/2,1/2,3/2,3/2,3/2],1,7797824,-1]);
> >> where H is the list of Dirichlet coefficients)
> >
> > I just tried this one:
> > <http://www.lmfdb.org/EllipticCurve/3.3.49.1/27.1/a/2>
> > and both PARI and LMFDB agreed.
> >
> > So someone should double check
> > <http://www.lmfdb.org/EllipticCurve/3.3.148.1/356.1/a/1>
> >
> > Cheers,
> > Bill.
> >