This morning, a mysterious user named "ranksunbounded" submitted the linked curve, which has rank at least thirty. This breaks the previous record of 29 found by Elkies and Klagsbrun in 2024.
Nobody knows whether it is possible to achieve arbitrarily high ranks.
Hehe, I really like them. And I always recommend those. It's not always that you have some nice books on deep concepts in mathematics for the "general" public
The rank of an elliptic curve is expected to be at most one by a combination of a simple heuristic from Cohen and Lenstra and a deep BSD consequence (but I think the case needed is known). However we know of families with rank 15, and sometimes those ranks go up at particular points.
The record before this morning was 29 and people suspected that was as high as it got. When we learn how this curve was obtained that might change.
I'm the maintainer of the linked website.
This morning, a mysterious user named "ranksunbounded" submitted the linked curve, which has rank at least thirty. This breaks the previous record of 29 found by Elkies and Klagsbrun in 2024.
Nobody knows whether it is possible to achieve arbitrarily high ranks.
Want to understand this more? Read the triplet of books by Ash and Gross, specially Elliptical Tales
Hehe, I really like them. And I always recommend those. It's not always that you have some nice books on deep concepts in mathematics for the "general" public
Can we have a tldr of the implications of this for the uninitiated?
The rank of an elliptic curve is expected to be at most one by a combination of a simple heuristic from Cohen and Lenstra and a deep BSD consequence (but I think the case needed is known). However we know of families with rank 15, and sometimes those ranks go up at particular points.
The record before this morning was 29 and people suspected that was as high as it got. When we learn how this curve was obtained that might change.