John Cremona on Sat, 30 Jul 2016 20:08:13 +0200 |
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Re: Support for elliptic curves over number fields |
Thanks Bill -- I will change the nfinit line and will report the L-function issue to the appropriate LMFDB-devs. 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. >