Timeline for How to explicitly compute lifting of points from an elliptic curve to a modular curve?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 11, 2014 at 23:14 | answer | added | Hao Chen | timeline score: 8 | |
| Aug 24, 2014 at 21:13 | comment | added | Maarten Derickx | See page 42 of math.harvard.edu/~elkies/modular.pdf | |
| Aug 24, 2014 at 21:12 | comment | added | Maarten Derickx | I would say that this question would even be interesting in the rank 1 case. For example in the easiest rank one case $E=X_0^+(37)$ exactly $9$ of the points in $E(\mathbb Q)$ are heegner points and one point corresponds to the exceptional 37 isogeny. These 10 points are the only 10 with integer j-invariant. So for all the other $p \in E(\mathbb Q)$ the pullbacks to $X_0(37)$ will give quadratic numbers fields, but the curves over these points won't be CM. The points in $E(Q)$ whose lift is not CM might still be Heegner points though, since a Heegner point is a sum of CM points. | |
| Feb 13, 2011 at 17:44 | comment | added | Ramsey | This reminds of a question that a friend and I tried to address some time ago. Namely, can one compute the polynomial $\prod(T-j(\alpha))$ where $\alpha$ varies over the fiber of such a modular parametrization. At the time, it seemed that computational resources weren't sufficient, but the situation may be different now. ...William? | |
| Feb 13, 2011 at 12:20 | answer | added | Chris Wuthrich | timeline score: 5 | |
| Feb 13, 2011 at 10:03 | history | asked | Kevin Buzzard | CC BY-SA 2.5 |