the analytic methods to be feasible. Not just mine
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...)
> 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)'