Fwd: strange elliptic curve error message

[daveloeffler]

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)'

[John Cremona]

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.l...@gmail.com>: