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| 2014-02-16 07:59:33 +0200 | asked a question | 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. |
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