#16022: simon_two_descent sometimes gives wrong answers
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Reporter: pbruin | Owner:
Type: defect | Status: new
Priority: critical | Milestone: sage-6.2
Component: elliptic | Keywords: simon_two_descent
curves | Authors: Peter Bruin
Merged in: | Report Upstream: Reported upstream. No
Reviewers: | feedback yet.
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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The current version of Denis Simon's 2-descent program (in Sage since
#11005) has a bug:
{{{
sage: K.<y> = NumberField(x^4 + x^2 - 7);
sage: E = EllipticCurve(K, [1, 0, 5*y^2 + 16, 0, 0])
sage: E.simon_two_descent(lim1=2, limtriv=3)
[0, 0, []]
}}}
The rank is in fact 1, and a correct return value would be `(1, 1,
[(-369/25*y^3 + 539/25*y^2 - 1178/25*y + 1718/25 : -27193/125*y^3 +
39683/125*y^2 - 86816/125*y + 126696/125 : 1)])`.
This ticket is just to fix this as quickly as possible; it should
eventually be fixed in a new version of Simon's program.
(See #15608 for a list of tickets related to `simon_two_descent`.)
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Ticket URL: <http://trac.sagemath.org/ticket/16022>
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