#4897: integral_points() misses some points
---------------------------+------------------------------------------------
Reporter: cremona | Owner: was
Type: defect | Status: new
Priority: major | Milestone: sage-3.4
Component: number theory | Keywords: elliptic curve integral points
---------------------------+------------------------------------------------
Francois Glineur reported to me that for the elliptic curve "20160bg2" not
all integral points are found.
{{{
sage: E=EllipticCurve('20160bg2')
sage: [P[0] for P in E.integral_points()]
[-24, -18, -14, -6, -3, 4, 6, 18, 21, 24, 36, 46, 102, 186, 1476, 2034,
67246]
}}}
while Magma gives
{{{
> E:=EllipticCurve([0, 0, 0, -468, 2592]);
> Sort([P[1] : P in IntegralPoints(E)]);
[ -24, -18, -14, -6, -3, 4, 6, 18, 21, 24, 36, 46, 102, 168, 186, 381,
1476, 2034, 67246 ]
}}}
so we are missing x=168 and x=381.
The curve has rank 2 and full 2-torsion.
The point Q=(168,2160) is the unique integral point its coset modulo
torsion and I think that is why it is being missed. In fact it seems
incredible that this has not been seen before in all the testing which was
done!
I therefore think that the function
integral_points_with_bounded_mw_coeffs() is at fault, and will fix it.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4897>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
--~--~---------~--~----~------------~-------~--~----~
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected]
To unsubscribe from this group, send email to
[email protected]
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en
-~----------~----~----~----~------~----~------~--~---
