Timeline for Rank of infinite family of elliptic curves over the rationals without assuming finiteness of Sha
Current License: CC BY-SA 4.0
3 events
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| Apr 26, 2023 at 9:05 | comment | added | EAg | Thank you! Yes, what I really had in mind is the open question! So there is no known infinite family of elliptic curves of rank exactly two over the rationals. | |
| Apr 26, 2023 at 8:55 | comment | added | Chris Wuthrich | Sure, take an elliptic surface whose rank over the base is $2$. Then by Silverman's specialisation theorem, all but finitely many fibres have rank at least $2$. As far as I know the open question is to have infinitely many elliptic curves over $\mathbb{Q}$ whose rank is exactly 2 | |
| Apr 26, 2023 at 8:44 | history | asked | EAg | CC BY-SA 4.0 |