Bill Allombert on Fri, 19 Apr 2013 11:17:26 +0200

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Re: Elliptic curve L-series limit problem

On Fri, Apr 19, 2013 at 08:14:47AM +0100, Allan MacLeod wrote:
> Hello,
> I am doing a lot of calculations which need to evaluate the derivative of the L-series of certain elliptic curves to reasonably high-precision. For curves with large conductor I need a large number of terms. I sometimes get the following error message
> anell for n>=%lu is not yet implemented
> I am using the Windows version of Pari-2.3.4, but can find no documentation about %lu.

This is an old bug: %lu is a placeholder for 2^24, which is the maximum length
of a vector on a 32bit system.

the documentation says:
? ?ellan
ellan(e,n): computes the first n Fourier coefficients of the L-function of the elliptic curve e
(n<2^24 on a 32-bit machine)

> Any advice or help would be much appreciated.

There are two solutions:
Either you run GP on a 64bit linux system which allow much longer vectors.
(unfortunately we do not support 64bit windows).

Or you change your program to use ellak instead for large values.
If this is too slow you can use ellap and a Buhler-Gross iteration
to loop over the an.

In any case, I would advise you to upgrade to a more recent PARI version, 
thought that will not fix this problem.