Timeline for Model of an elliptic curve with p-torsion
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Apr 6, 2022 at 10:46 | comment | added | Joe Silverman | @FrançoisBrunault Thanks, that's probably the paper that I was trying to recall when I mentioned Mordell's name. | |
| Apr 6, 2022 at 10:08 | vote | accept | did | ||
| Apr 6, 2022 at 9:01 | comment | added | François Brunault | This method has been used before, not with the aim to find equations of $X_1(N)$, but to determine elliptic curves over $\mathbb{Q}$ with a given torsion subgroup. For example Billing and Mahler in "On exceptional points on cubic curves" (Journal of the LMS, vol. 15, 1940) showed that an elliptic curve over $\mathbb{Q}$ cannot have a rational point of order $11$. In the course of doing so, they prove in Lemma 2 (p. 41) that a certain cubic curve with explicit equation has exactly 5 rational points, the curve being of course $X_1(11)$. | |
| Apr 5, 2022 at 20:55 | history | answered | Joe Silverman | CC BY-SA 4.0 |