id summary reporter owner description type status priority milestone component resolution keywords cc merged author reviewer upstream work_issues branch commit dependencies stopgaps
27015 bugs in integral_points for elliptic curves over QQ cremona "The code for computing all integral points on elliptic curves over QQ has bugs, some due to incorrect formulas in the literature. For example:
{{{
sage: E = EllipticCurve('2082a1')
sage: E.integral_points()
[(-11 : 29 : 1), (-2 : 29 : 1), (4 : 11 : 1), (13 : 29 : 1)]
sage: E([507525709, 11433453531221, 1])
(507525709 : 11433453531221 : 1)
}}}
This curve has rank 1 and trivial torsion, generator P=(13,-43) and the integral points are k*P for k=1,2,3,4 and 13 (and their negatives). We miss 13*P because the upper bound computed is only 12 (as seen with verbose=True).
#10973 implements integral points on elliptic curves over arbitrary number fields, and also provides a fix for this bug since it work over QQ (the branch at #10973 has the integral_points() method over QQ call the general one). However the code there is slow over QQ (and relies on some incorrect though published assumptions). Hence there is a case for fixing the bugs over QQ independently of the general implementation, and that will be done here." defect new major elliptic curves elliptic curves, integral points John Cremona N/A