Timeline for Polynomial sparsity of conductors of elliptic curves
Current License: CC BY-SA 4.0
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| Aug 25, 2021 at 23:01 | comment | added | alpoge | If you believe ranks are uniformly bounded (or even just really small in terms of the minimal discriminant) then yeah, check out Corollary 3.11 of Helfgott-Venkatesh arxiv.org/pdf/math/0405180.pdf and apply it to the handful of Mordell curves you get in the usual argument that there are only finitely many elliptic curves over a number field of given conductor. (Lemme know if I’ve confused myself though!) | |
| Aug 25, 2021 at 16:44 | comment | added | Will Sawin | Probably no such $P$ exists, but it might already be nontrivial to prove there does not exist a linear such $P$. | |
| Aug 25, 2021 at 7:19 | history | asked | Matias2 | CC BY-SA 4.0 |