Timeline for Rank of $x (x^2 - 1) = c (c^2 - 1) y^2 $ over $\mathbb{Q}$ for given rational values of $c$
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Jun 18, 2012 at 2:34 | comment | added | Noam D. Elkies | That's the general quadratic twist $Dy^2 = x^3 - x$ of the "congruent-number curve" $y^2 = x^3 - x$, subject to the condition that it have a point of infinite order (the point cannot be torsion for any rational $c \neq 0, \pm 1$). The behavior of the rank is a well-known open question. The current record is $7$; Nick Rogers found the first example some years ago. | |
| Jun 18, 2012 at 0:58 | answer | added | Joseph O'Rourke | timeline score: 2 | |
| Jun 17, 2012 at 20:11 | answer | added | Remke Kloosterman | timeline score: 16 | |
| Jun 17, 2012 at 18:17 | history | edited | John R Ramsden | CC BY-SA 3.0 |
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| Jun 17, 2012 at 18:11 | history | asked | John R Ramsden | CC BY-SA 3.0 |