Thank you both for the answers, I found another problematic example
sage:E1=EllipticCurve([0,0,0,37,18]);E1;S=E1.integral_points();S; Elliptic Curve defined by y^2 = x^3 + 37*x + 18 over Rational Field [(2 : 10 : 1), (126 : 1416 : 1)] and R = E1(64039202,512470496030);M=E1(2,10 );3*M==R True Both examples are from the paper of Don Zagier: Large integral points on Elliptic curves <http://people.mpim-bonn.mpg.de/zagier/files/doi/10.2307/2007900/fulltext.pdf> Also, I tried the previous examples in the online calculator of magma and seems that magma works fine. magma: E := EllipticCurve([0,0,0,37,18]); IntegralPoints(E); [ (2 : 10 : 1), (126 : 1416 : 1), (64039202 : 512470496030 : 1) ] [ <(2 : 10 : 1), 1>, <(126 : 1416 : 1), 1>, <(64039202 : 512470496030 : 1), 1> ] I use this function a lot and I think many people (heavily) use this function for their research. I was not aware of the problems of this function :( I am wondering if this bug affects other functions concerning elliptic curves? Thanks again for the answers Costas. On Wednesday, December 14, 2016 at 10:25:25 PM UTC+2, Nils Bruin wrote: > > On Wednesday, December 14, 2016 at 12:09:36 PM UTC-8, John Cremona wrote: >> >> >> Thanks for the bug report. As Nils pointed out there are known bugs >> in the integral point code which cause solutions to be missed. > > > Just to make clear: I wasn't taking a jibe at sage/or John on this, and I > wasn't previously aware there are bugs in the integral points code in Sage. > I was just observing that in the past 20 years, any computer algebra > package that implements integral point finding on elliptic curves has had > significant errors (of the type reported here). Apparently it's something > that is particularly hard to get reliably correct. > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
