#15667: Time anomaly in finding orders of points on an elliptic curve over a
finite
field
-------------------------------------+-------------------------------------
Reporter: cremona | Owner:
Type: defect | Status: positive_review
Priority: major | Milestone: sage-6.2
Component: elliptic curves | Resolution:
Keywords: point order | Merged in:
finite field | Reviewers: Jean-Pierre Flori
Authors: John Cremona | Work issues:
Report Upstream: N/A | Commit:
Branch: | c5c2d0c78863349d959609df700decbff9dc43fe
u/jpflori/ticket/15667 | Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Comment (by cremona):
Preliminary diagnosis: the elliptic curve E in the report is defined over
{{{GF(3^6)}}} and has j-invariant 0=1728. The special case code to give
the cardinality in this case starts at line 574 of
{{{sage/schemes/elliptic_curves/ell_finite_field.py}}}, which I wrote in
2008. The code incorrectly gives group order 703 while it is in fact
{{{
sage: F.<a>=GF(3^6,'a')
sage: E = EllipticCurve([a^5 + 2*a^3 + 2*a^2 + 2*a, a^4 + a^3 + 2*a + 1])
sage: E.cardinality_exhaustive()
784
}}}
compared with
{{{
sage: F.<a>=GF(3^6,'a')
sage: E = EllipticCurve([a^5 + 2*a^3 + 2*a^2 + 2*a, a^4 + a^3 + 2*a + 1])
sage: E.cardinality()
703
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/15667#comment:7>
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