On 17 September 2014 13:04, Jeroen Demeyer <[email protected]> wrote:
> On 2014-09-17 11:16, John Cremona wrote:
>>
>> I hope you are right, as that would be good news -- it used to have
>> greater overheads.  On the other hand, in your tests you were reusing
>> the same large finite field many times, and using large fields, wheras
>> the typical case for me (e.g. for evaluating L-functions) is to get
>> E.ap(p) for all p up to some bound
>
> You could use the Sage function E.aplist() which does precisely this.

Surre -- only over Q though.  Over number fields we get into the swamp
of deciding how to order the primes...

I am currently testing these functions (which will be added to the
class for elliptic curves over number fields):

Euler_polynomial(E,P) # P a prime of the number field
rational_Euler_polynomail(E,p) # p a rational prime
rational_L_coefficients(E,nmax,prime_powers_only=True) # n'th
coefficients of the L-series for n up to nmax

which I am using to sort isogeny classes for the LMFDB.

John


>
> Alternatively, if you want to avoid Sage overhead, you could directly call
> the PARI functions.
>
>
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