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Fwd: strange elliptic curve error message
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daveloeffler  
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 More options Sep 29, 9:48 am
From: daveloeffler <dave.loeff...@gmail.com>
Date: Tue, 29 Sep 2009 06:48:48 -0700 (PDT)
Local: Tues, Sep 29 2009 9:48 am
Subject: Fwd: strange elliptic curve error message
Kevin Buzzard just told me about this rather weird error he'd got:

> If I fire up sage (version 4.0.1) and then type

> E = EllipticCurve([0,-39409298,0,5554231502,0])
> E.analytic_rank()

> (which, to be honest, I don't expect to terminate) then I get a RuntimeError.
> I thought that the yoga was "just read the last line if you're not an expert".
> The last line says

> RuntimeError: error '  ***   error opening input file: /home/buzzard/.sage/
>                                   ^--------------------' running 'ellanalyticrank(ellinit([0, 1, 0, -517692035386099,
> -4533726894914038913619]),0)'

> ??

I got the same error in 4.1.2.alpha4. The full traceback (below)
suggests that this has something to with the code in extcode/pari/
cremona; but it would be nice if it could fail a bit more gracefully!

sage: E = EllipticCurve([0,-39409298,0,5554231502,0])
sage: E.analytic_rank()
---------------------------------------------------------------------------
RuntimeError                              Traceback (most recent call
last)

/home/david/.sage/temp/rockhopper/5225/
_home_david__sage_init_sage_0.py in <module>()

/home/david/sage-4.1.2.alpha4/local/lib/python2.6/site-packages/sage/
schemes/elliptic_curves/ell_rational_field.pyc in analytic_rank(self,
algorithm)
   1354
"""
   1355         if algorithm ==
'cremona':
-> 1356             return rings.Integer(gp_cremona.ellanalyticrank
(self.minimal_model().a_invariants()))
   1357         elif algorithm ==
'rubinstein':
   1358
try:

/home/david/sage-4.1.2.alpha4/local/lib/python2.6/site-packages/sage/
schemes/elliptic_curves/gp_cremona.pyc in ellanalyticrank
(e)
    100     while
True:
    101
try:
--> 102             return ellanalyticrank_prec(e,
prec)
    103         except
RuntimeError,msg:
    104             if 'precision too low' in str
(msg):

/home/david/sage-4.1.2.alpha4/local/lib/python2.6/site-packages/sage/
schemes/elliptic_curves/gp_cremona.pyc in ellanalyticrank_prec(e,
prec)
     74     if prec: gp.set_real_precision
(old_prec)
     75     if x.find("***") !=
-1:
---> 76         raise RuntimeError, "error '%s' running '%s'"%
(x,cmd)
     77     return Integer
(x)

78

RuntimeError: error '  ***   error opening input file: /home/
david/.sage//t
                                  ^--------------------' running
'ellanalyticrank(ellinit([0, 1, 0, -517692035386099,
-4533726894914038913619]),0)'


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John Cremona  
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 More options Sep 29, 12:36 pm
From: John Cremona <john.crem...@gmail.com>
Date: Tue, 29 Sep 2009 17:36:41 +0100
Local: Tues, Sep 29 2009 12:36 pm
Subject: Re: [sage-nt] Fwd: strange elliptic curve error message
That curve has conductor 138017814149445394258041472 = 2^7 * 7 * 2339
* 11621 * 1187309 * 4772980417 which is just far too big for any of
the analytic methods to be feasible.  Not just mine
(algorithm="cremona", the default -- though not the best!) but also
"rubinstein" and "sympow" fail.

mwrank gives an upper bound of 3, and the root number is -1.  I guess
you would like to know whether the rank is 1 or 3.  It does not seem
easy to find any rational points (apart from the one of order 2...)

John

2009/9/29 daveloeffler <dave.loeff...@gmail.com>:


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