Opened 10 years ago

Last modified 10 years ago

#10730 closed defect

simon_two_descent -- reports points as being independent, but they are not — at Initial Version

Reported by: was Owned by: davidloeffler
Priority: minor Milestone: sage-duplicate/invalid/wontfix
Component: elliptic curves Keywords:
Cc: Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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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
sage: v = E.simon_two_descent()
sage: P,Q =v[2]
sage: Q == 4*P
sage: P.order()
sage: Q.order()

So instead of claiming the output points are independent, claim nothing about them?

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