Timeline for Can we use this formula to construct rational points on the curve $C$?
Current License: CC BY-SA 3.0
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| Jun 5, 2014 at 15:43 | comment | added | ACL | Then this looks worse. Set $\nu=f^{(m)}(1)/h(S)$; the question begins: from a rational point of infinite order, construct other points. | |
| Jun 5, 2014 at 15:38 | comment | added | Safwane | @ACL: There is an error in the question: the constant is $v$ without known relation to rational numbers. | |
| Jun 5, 2014 at 15:36 | history | edited | Safwane | CC BY-SA 3.0 |
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| Jun 5, 2014 at 13:03 | vote | accept | Safwane | ||
| Jun 5, 2014 at 11:27 | answer | added | Joe Silverman | timeline score: 1 | |
| Jun 5, 2014 at 10:29 | comment | added | ACL | In view of the BSD conjecture, $f^{(m)}(1)$ should be related to the regulator of the elliptic curve, i.e., a determinant made from heights of points out of a basis of the Mordell-Weil group (mod torsion). So it looks unlikely that one could prove that $f^{(m)}(1)$ is a rational multiple of the height of a single point. | |
| Jun 5, 2014 at 10:02 | history | edited | Safwane | CC BY-SA 3.0 |
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| Jun 5, 2014 at 9:25 | history | edited | Safwane | CC BY-SA 3.0 |
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| Jun 5, 2014 at 9:19 | history | asked | Safwane | CC BY-SA 3.0 |