Benyamin Gholami on Fri, 17 Feb 2017 10:37:16 +0100

• To: Benyamin Gholami <benyamingholami10@gmail.com>, pari-users@pari.math.u-bordeaux.fr
• From: Benyamin Gholami <benyamingholami10@gmail.com>
• Date: Fri, 17 Feb 2017 13:07:04 +0330
• Delivery-date: Fri, 17 Feb 2017 10:37:16 +0100
• References: <CACvE4G8YSrZj_VubL8P6UvpDw-AGnmiUQDPkn2WchGbuM1ps3Q@mail.gmail.com> <20170117163821.GA27452@math.u-bordeaux.fr> <CACvE4G-vuFvEP4HSR+hnjN1Ood93HteZm1o0qppKHLWw6ar6HA@mail.gmail.com>

hi sir . i asked you a question for computing mestre sum for elliptic curves and you gave me very good answer . you send me the code :
S(E, N) =
{ my (s = 0.0);
forprime(p = 2, N, my(a = ellap(E,p)); s += (2-a)/(p+1-a));
return (s);
}

now i want to compute this sum for some fibrations of elliptic surfaces and choose those that have large sum . for example if we have :
y^2=x^3+t*x^2+t*x+1  i want to compute above sum for curves with -100<t<100 with integer t and then compute S(E_t,N) for all of this curve witch E_t is above surface with prescribed t and then pari print the value of sum and related t for the curve so that i can choose best of them . how can write the codes in pari ?
can you help me?

On Tue, Jan 17, 2017 at 8:20 PM, Benyamin Gholami wrote:
i dont know how to thank you

On Tue, Jan 17, 2017 at 8:08 PM, Karim Belabas wrote:
* Benyamin Gholami [2017-01-17 15:18]:
> hi
> i want to calculate mestre sum S(E,N) for elliptic curves:
>  \sum ((-a_p)+2)/(p+1-(a_p))
> but i don't know its code in pari or sage .
> how can i do this?

I'm not sure what S(E,N) is; here's a guess:

S(E, N) =
{ my (s = 0.0);
forprime(p = 2, N, my(a = ellap(E,p)); s += (2-a)/(p+1-a));
return (s);
}

(17:37) gp > E = ellinit([0,0,0,1,1]); \\ y^2 = x^3 + x + 1
(17:37) gp > S(E, 10^6)
time = 2,188 ms.
%2 = 4.8147746248168721613546571313173856035

Cheers,

K.B.
--
Karim Belabas, IMB (UMR 5251)  Tel: (+33) (0)5 40 00 26 17
Universite de Bordeaux         Fax: (+33) (0)5 40 00 21 23
351, cours de la Liberation    http://www.math.u-bordeaux.fr/~kbelabas/
F-33405
Talence (France)       http://pari.math.u-bordeaux.fr/  [PARI/GP]
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