Pierre Charollois on Sun, 13 Feb 2022 13:25:45 +0100


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Re: miller functions for elliptic curves

Thanks ! 
It is not exactly what I need, but it is helpful.

Best,

Pierre

Le ven. 4 févr. 2022 à 17:55, Bill Allombert <Bill.Allombert@math.u-bordeaux.fr> a écrit :
On Fri, Feb 04, 2022 at 05:16:52PM +0100, Pierre Charollois wrote:
> I need a function with  divisor m[P] - m[OE], for an elliptic curve over Q,
> and P, Q  arbitrary torsion points.
> I can probably code this naively myself, but maybe there are for instance
> tricks that reduce the number of iterations. (I noticed papers about this).

Most of the papers are for the evaluated version.  For the non-evaluated
version, speed is limited by the size of the output.

You can try the attached script (based on an old script by John Cremona).

E=ellinit("11a1");
P=[5,5]
ellorder(E,P)
f=ellweilpol(E,P,5)

%12 =(150*x^3+(-35*y-2075)*x^2+(-4*y^2+390*y+9400)*x+(y^3+5*y^2-1000*y-14000))/(x^2-32*x+256)

Is it waht you need ?

Cheers,
Bill.