| 34 | |

| 35 | |

| 36 | You will get the correct output for the first few primes, but the error message, which in the above case occurs above the prime ideal (67), is |

| 37 | |

| 38 | |

| 39 | Traceback (most recent call last): |

| 40 | File "<stdin>", line 1, in <module> |

| 41 | File "_sage_input_8.py", line 10, in <module> |

| 42 | exec compile(u'open("___code___.py","w").write("# -*- coding: utf-8 -*-\\n" + _support_.preparse_worksheet_cell(base64.b64decode("dGVzdChGLCAxMDAp"),globals())+"\\n"); execfile(os.path.abspath("___code___.py")) |

| 43 | File "", line 1, in <module> |

| 44 | |

| 45 | File "/tmp/tmpVYbgxh/___code___.py", line 3, in <module> |

| 46 | exec compile(u'test(F, _sage_const_100 ) |

| 47 | File "", line 1, in <module> |

| 48 | |

| 49 | File "/tmp/tmptawaYw/___code___.py", line 14, in test |

| 50 | print "at %s with %d points in the reduced curve"%(factors[j][_sage_const_0 ], curve.reduction(factors[j][_sage_const_0 ]).count_points() ) |

| 51 | File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/schemes/elliptic_curves/ell_finite_field.py", line 322, in count_points |

| 52 | return self.cardinality() |

| 53 | File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/schemes/elliptic_curves/ell_finite_field.py", line 951, in cardinality |

| 54 | self._order = self.cardinality_bsgs() |

| 55 | File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/schemes/elliptic_curves/ell_finite_field.py", line 1220, in cardinality_bsgs |

| 56 | N1 = ZZ(2)**sum([e for P,e in E1._p_primary_torsion_basis(2)]) |

| 57 | File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/schemes/elliptic_curves/ell_generic.py", line 2660, in _p_primary_torsion_basis |

| 58 | Ep = self(0).division_points(p) |

| 59 | File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/schemes/elliptic_curves/ell_point.py", line 879, in division_points |

| 60 | Q = E.lift_x(x) |

| 61 | File "/usr/local/sage2/local/lib/python2.6/site-packages/sage/schemes/elliptic_curves/ell_generic.py", line 855, in lift_x |

| 62 | raise ValueError, "No point with x-coordinate %s on %s"%(x, self) |

| 63 | ValueError: No point with x-coordinate 39*tbar + 11 on Elliptic Curve defined by y^2 = x^3 + 2*x^2 + (2*ubar+4)*x + (2*ubar+3) over Residue field in ubar of Fractional ideal (67) |