Opened 10 years ago
Closed 10 years ago
#10730 closed defect (duplicate)
simon_two_descent -- reports points as being independent, but they are not
Reported by: | was | Owned by: | davidloeffler |
---|---|---|---|
Priority: | minor | Milestone: | sage-duplicate/invalid/wontfix |
Component: | elliptic curves | Keywords: | |
Cc: | Merged in: | ||
Authors: | Reviewers: | Robert Miller | |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
Check out this
sage: F.<a> = NumberField(x^2-x-1) sage: E = EllipticCurve([1,a+1,a,a,0]) sage: E.simon_two_descent() (0, 1, [(-1 : -a + 1 : 1), (-a : 0 : 1)])
According to the docs:
Computes lower and upper bounds on the rank of the Mordell-Weil group, and a list of independent points.
It output a lower bound of 0, an upper bound of 1, and gave *two* independent points? Clearly something is wrong. In fact, the points output are all torsion and one is a multiple of the other:
sage: E.torsion_subgroup() Torsion Subgroup isomorphic to Z/8 associated to the Elliptic Curve defined by y^2 + x*y + a*y = x^3 + (a+1)*x^2 + a*x over Number Field in a with defining polynomial x^2 - x - 1 sage: Q == 4*P True sage: v = E.simon_two_descent() sage: P,Q =v[2] sage: Q == 4*P True sage: P.order() 8 sage: Q.order() 2
So instead of claiming the output points are independent, claim nothing about them?
This is a duplicate of #5153.
Change History (4)
comment:1 in reply to: ↑ description ; follow-up: ↓ 2 Changed 10 years ago by
comment:2 in reply to: ↑ 1 Changed 10 years ago by
Incidentally, from a 2-(isogeny-)descent on E one can conclude that the rank is 0, so while the upper bound returned does not contradict the documentation, the code is not returning the appropriate bound. In Magma:
RankBound?(EllipticCurve?([1,a+1,a,a,0]));
0
AnalyticRank?(E);
0 0.359929 but you probably already knew that.
comment:3 Changed 10 years ago by
See #5153
comment:4 Changed 10 years ago by
- Component changed from number fields to elliptic curves
- Description modified (diff)
- Milestone changed from sage-4.7.2 to sage-duplicate/invalid/wontfix
- Resolution set to duplicate
- Reviewers set to Robert Miller
- Status changed from new to closed
Since it's doing a 2-descent the code should be able to guarantee that the points returned generate E(k)/2E(k) and should be able to test that the points form a basis of E(k)/2E(k) as an F_2-vector space. That's a kind of independence ...