#13163: E.minimal_model() crashes with large coefficients.
-------------------------------+--------------------------------------------
   Reporter:  weigandt         |             Owner:  cremona      
       Type:  defect           |            Status:  new          
   Priority:  major            |         Milestone:  sage-5.2     
  Component:  elliptic curves  |          Keywords:  minimal model
Work issues:                   |   Report Upstream:  N/A          
  Reviewers:                   |           Authors:               
  Merged in:                   |      Dependencies:               
   Stopgaps:                   |  
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 This code

 {{{
 E=EllipticCurve([4382696457564794691603442338788106497, 28, 3992,
 16777216, 298])
 E.minimal_model()
 }}}

 Spits out this error:

 {{{
 Traceback (most recent call last):
   File "<stdin>", line 1, in <module>
   File "_sage_input_23.py", line 10, in <module>
     exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8
 -*-\\n" +
 
_support_.preparse_worksheet_cell(base64.b64decode("RT1FbGxpcHRpY0N1cnZlKFs0MzgyNjk2NDU3NTY0Nzk0NjkxNjAzNDQyMzM4Nzg4MTA2NDk3LCAyOCwgMzk5MiwgMTY3NzcyMTYsIDI5OF0pCkUubWluaW1hbF9tb2RlbCgp"),globals())+"\\n");
 execfile(os.path.abspath("___code___.py"))
   File "", line 1, in <module>

   File "/tmp/tmpQWTtgb/___code___.py", line 4, in <module>
     exec compile(u'E.minimal_model()
   File "", line 1, in <module>

   File
 "/sagenb/sage_install/sage-5.0-boxen-x86_64-Linux/local/lib/python2.7
 /site-packages/sage/schemes/elliptic_curves/ell_rational_field.py", line
 2552, in minimal_model
     F = self.pari_mincurve()
   File
 "/sagenb/sage_install/sage-5.0-boxen-x86_64-Linux/local/lib/python2.7
 /site-packages/sage/schemes/elliptic_curves/ell_rational_field.py", line
 713, in pari_mincurve
     e = self.pari_curve(prec)
   File
 "/sagenb/sage_install/sage-5.0-boxen-x86_64-Linux/local/lib/python2.7
 /site-packages/sage/schemes/elliptic_curves/ell_rational_field.py", line
 664, in pari_curve
     self._pari_curve[prec] =
 pari(list(self.a_invariants())).ellinit(precision=prec)
   File "gen.pyx", line 10416, in sage.libs.pari.gen._pari_trap
 (sage/libs/pari/gen.c:49843)
 sage.libs.pari.gen.PariError: precision too low (10)
 }}}

 It looks like the precision needs to be increased when such a large curve
 is fed to PARI's minimal model algorithm.

-- 
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/13163>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica, 
and MATLAB

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