Timeline for Why is this "the first elliptic curve in nature"?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| May 20, 2020 at 14:08 | comment | added | François Brunault | PS. I think what I wrote is conditional on Stevens's conjecture on the Manin constant of $X_1(N)$-parametrisations. | |
| May 20, 2020 at 14:06 | comment | added | François Brunault | For each isogeny class of elliptic curves over $\mathbb{Q}$, one can define a graph (which I believe is canonical) where the vertices are the elliptic curves and the arrows are the étale isogenies of prime degree. Étale means, for example, that the pull-back preserves the Néron differentials. It turns out that this graph is a tree, and the root is the $X_1(N)$-minimal curve (the smallest degree of $X_1(N) \to E$). So there is a unique curve with smallest Faltings height. This last property can fail over number fields. | |
| May 20, 2020 at 13:00 | comment | added | David Roberts♦ | From (nearly) the horse's mouth! Unless Cremona lets us know why, this might be as good as we get (if you can get him to explain, I would be curious to know). | |
| May 20, 2020 at 12:18 | review | First posts | |||
| May 20, 2020 at 12:35 | |||||
| May 20, 2020 at 12:17 | history | answered | Nicolas Mascot | CC BY-SA 4.0 |