Re: Support for elliptic curves over number fields

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

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)

Cheers,
Bill.