Timeline for Rational points on the elliptic curve $y^2 = x^{3} - t^{2}z^3$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Aug 16, 2020 at 22:08 | comment | added | Thomas | True. I left that up to the OP which way (s)he wanted to organize the solutions | |
| Aug 16, 2020 at 15:23 | comment | added | Will Sawin | It's not (just) about the number of variables, but rather that the equation defines a rational variety (which is in part caused by the fact that it is a degree $3$ equation in $4$ variables). After the change of variables in the first line, can't you finish by writing $z = \frac{x^3-y^2}{v^2}$ as a function of the other variables? (so $t = \frac{v^3}{ x^3-y^2}$ completes the parametric solution.) | |
| Aug 12, 2020 at 10:32 | history | edited | Thomas | CC BY-SA 4.0 |
added 450 characters in body
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| Aug 12, 2020 at 5:49 | history | answered | Thomas | CC BY-SA 4.0 |