Re: Support for elliptic curves over number fields

[Bill Allombert <Bill.Allombert@math.u-bordeaux.fr>]

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.