John Cremona on Fri, 17 Feb 2017 16:42:57 +0100

for(t=-10,10, E=ellinit([0,t,0,t,1]); if(E==[],,print(t,": ",S(E,100))))

On 17 February 2017 at 09:37, Benyamin Gholami
<benyamingholami10@gmail.com> wrote:
> 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
> <benyamingholami10@gmail.com> wrote:
>>
>> i dont know how to thank you
>>
>> On Tue, Jan 17, 2017 at 8:08 PM, Karim Belabas
>> <Karim.Belabas@math.u-bordeaux.fr> 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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