#15483: Simon 2-descent gives RuntimeError for an elliptic curve over a
quadratic
field
-------------------------------+-------------------------------------
Reporter: pbruin | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-5.13
Component: elliptic curves | Keywords: simon_two_descent
Merged in: | Authors:
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
-------------------------------+-------------------------------------
The following tries to do 2-descent on an elliptic curve over a quadratic
field:
{{{
K.<s>=QuadraticField(229)
c4=2173-235*(1-s)/2
c6=-124369+15988*(1-s)/2
E=EllipticCurve([-c4/48,-c6/864])
E.simon_two_descent()
}}}
It fails with a `RuntimeError`:
{{{
Traceback (most recent call last):
...
RuntimeError:
*** at top-level: ans=bnfellrank(K,[0,0,0,
*** ^--------------------
*** in function bnfellrank: ...eqtheta,rnfeq,bbnf];rang=
*** bnfell2descent_gen(b
*** ^--------------------
*** in function bnfell2descent_gen: ...riv,r=nfsqrt(nf,norm(zc))
*** [1];if(DEBUGLEVEL_el
*** ^--------------------
*** array index (1) out of allowed range [none].
An error occurred while running Simon's 2-descent program
}}}
It appears that a certain number field element is expected to be a square,
but in fact isn't.
The bug is not fixed by first changing to an integral model.
--
Ticket URL: <http://trac.sagemath.org/ticket/15483>
Sage <http://www.sagemath.org>
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