ASKSAGE: Sage Q&A Forum - Latest question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 16 Feb 2014 00:59:33 -0600procedure integralpoints produces wrong answerhttp://ask.sagemath.org/question/11045/procedure-integralpoints-produces-wrong-answer/Elliptic Curve E defined by y^2 = x^3 - 4627*x + 13870 over Rational Field, rank=4
The procedure E.integral_points(verbose=True) uses a MW basis which isn't a basis. Therefore the answer is not correct. There are at least 60 integral points on this curve, but the procedure finds only 58 points. In fact the pair E(1676505139935,±2170737625086802600) is missing. The value of the regulator of the four basis points used in the procedure is 4 times the value of the regulator of four correct basis points. Strange enough the above missing points are linear combinations of the four basis points used in the procedure. I have more examples with similar errors. I used the SAGE app version 6.1.1 on OSX Maverick as well as SAGE version 5.13 in a Virtual Box under Windows 7.RoelSun, 16 Feb 2014 00:59:33 -0600http://ask.sagemath.org/question/11045/