Timeline for Torsion points on $E/\mathbb{Q}$ with large coordinates
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 16, 2021 at 20:58 | answer | added | Joe Silverman | timeline score: 10 | |
| May 16, 2021 at 18:27 | comment | added | user166831 | Rank 0 means the points are torsion, and there are only finitely many by Mordell's theorem. If $E$ is in Weierstrass form with integer coefficients and $(x:y:1)$ is a torsion point, then either $y=0$ or it divides the discriminant (Lutz-Nagell). | |
| May 16, 2021 at 17:01 | comment | added | folenn | @NoamD.Elkies I see. What if we just require the rank to be zero? | |
| May 16, 2021 at 17:01 | history | edited | folenn | CC BY-SA 4.0 |
added 6 characters in body; edited title
|
| May 16, 2021 at 16:43 | comment | added | Noam D. Elkies | Can't happen if you put $E$ in Weierstrass form $y^2 = P(x)$ because the 2-torsion points are just $(x,0)$ where $x$ is one of the zeros of $P$. | |
| May 16, 2021 at 14:11 | review | First posts | |||
| May 16, 2021 at 14:26 | |||||
| May 16, 2021 at 14:07 | history | asked | folenn | CC BY-SA 4.0 |