This seems to me like a bug with Sage. I have attached a point on an elliptic curve over a finite field for which this problem occurs to this message. Running Sage in the directory containing the point gives the following:
sage: from sage.misc.persist import load
sage: P = load("point")
sage: P.order()
^C
---------------------------------------------------------------------------
KeyboardInterrupt Traceback (most recent call last)
<ipython-input-3-e60806397b1c> in <module>()
----> 1 P.order()
/usr/lib/python2.7/site-packages/sage/schemes/elliptic_curves/ell_point.pyc
in order(self)
3519 E = self.curve()
3520 ord = getattr(E, "_order", None) # get cached order of the
curve
-> 3521 return Integer(E.pari_curve().ellorder(self, ord))
3522
3523 additive_order = order
cypari2/auto_gen.pxi in cypari2.gen.Gen_base.ellorder()
KeyboardInterrupt:
sage: P.curve().order()
18061112346694138117304349799948434434304
sage: P.order()
11
sage:
Here I interrupt P.order() after waiting for a long time, yet if I first
run P.curve().order() the command P.order() runs quickly.
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point.sobj
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