[Zhibin Liang]

Dear all,

I rank the following sage programme and ask the analytic rank for E.
Can someone explain what happens to this function?

BTW, it works for small conductor E.





sage: E=EllipticCurve([0, 73596504392, 0, 1269479404387892646015, 0])
sage:
sage: print E.analytic_rank()
---------------------------------------------------------------------------
PariError Traceback (most recent call last)

/home/liangzhb/<ipython console> in <module>()

/usr/local/sage/sage-5.3/local/lib/python2.7/site-packages/sage/schemes/elliptic_curves/ell_rational_field.pyc
in analytic_rank(self, algorithm, leading_coefficient)
1343 """
1344 if algorithm == 'pari':
-> 1345 rank_lead = self.pari_curve().ellanalyticrank()
1346 if leading_coefficient:
1347 return (rings.Integer(rank_lead[0]),
rank_lead[1].python())

/usr/local/sage/sage-5.3/local/lib/python2.7/site-packages/sage/libs/pari/gen.so
in sage.libs.pari.gen._pari_trap (sage/libs/pari/gen.c:54863)()

PariError: not enough precomputed primes (19)


--

Very best wishes
Zhibin Liang

Homepage (Outside of China):
Chinese http://wstein.org/home/liangzhb/web/
English http://wstein.org/home/liangzhb/web/En.htm




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[Alex Ghitza]

Hi,

On Tue, Oct 2, 2012 at 9:45 AM, Zhibin Liang <lian...@gmail.com> wrote:
> I rank the following sage programme and ask the analytic rank for E.
> Can someone explain what happens to this function?

> sage: E=EllipticCurve([0, 73596504392, 0, 1269479404387892646015, 0])
> sage:
> sage: print E.analytic_rank()
> ---------------------------------------------------------------------------
> PariError Traceback (most recent call last)
>

> PariError: not enough precomputed primes (19)

As the message says, "not enough precomputed primes". Here are more
details: when the pari interpreter starts, it precomputes the list of
the first N primes. This list is used in a number of the pari
functions, including the function that computes the analytic rank of
an elliptic curve. If the computation is large, it may happen that
pari needs some primes that are larger than what is on its list, in
which case it gives the error message that you saw.

The way to go past this obstacle is to increase the list of
precomputed primes. You do this from Sage as follows:

sage: pari.init_primes(10^7)

and then you try your computation again:

sage: E.analytic_rank()

I've just tried this and the error message is gone. Of course, it's
taking forever, which is not very surprising since the conductor of E
is pretty big (23 digits).

--
Best,
Alex

--
Alex Ghitza -- Lecturer in Mathematics -- The University of Melbourne
http://aghitza.org

[Zhibin Liang]

Alex , Thank you .

2012/10/2 Alex Ghitza <agh...@gmail.com>:

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--

Very best wishes
Zhibin Liang