|Bill Allombert on Thu, 28 Jul 2016 00:40:15 +0200|
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|Re: Support for elliptic curves over number fields|
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.