Bill Allombert on Sat, 16 Jul 2016 19:46:53 +0200 |
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Re: Support for elliptic curves over number fields |
On Sat, Jul 16, 2016 at 05:44:07PM +0100, John Cremona wrote: > On 16 July 2016 at 17:06, Bill Allombert > <Bill.Allombert@math.u-bordeaux1.fr> wrote: > > Dear PARI developers, > > > > We have added basic support for elliptic curves over number fields and L > > function of elliptic curves over number fields. > > Excellent! Some of this functionality is already mentioned on web > pages such as http://www.lmfdb.org/EllipticCurve/3.3.148.1/356.1/a/1 > (after clicking the "Show commands for ... Pari/gp" near the top. If > those commands are not correct, please let me know (they were written > by Aurel). I notice that he did not include the field as a parameter > in the ellinit(). > > > > > This is an example: > > > > ? N=nfinit(a^3-26); > > ? E=ellinit([a,0,1,0,0],N); > > ? lfun(E,1) > > %4 = 0.24961216776576924744553489082015201012 > > Are there plans to include Denis Simon's gp scripts for 2-descent, > over Q and over number fields, as standard? Yes, but this requires changes to the way S-units of number fields are computed. Cheers, Bill.