alt Hacker NewsThe 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.
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pirates • today at 3:29 PM
BSD == Birch and Swinnerton-Dyer I think? I am also uninitiated. I enjoy learning about the millennium prize problems but BSD is one I don’t have a very good understanding of.
> The record before this morning was 29 and people suspected that was as high as it got.
Exactly this. A fundamental question in the subject is, whether elliptic curve ranks are bounded. Contrast with e.g. prime numbers, of which are known to be infinitely many. If you set a new record for the largest known prime, then that's cool but everyone knew there were plenty out there to discover.
This paper, by leading experts,
https://arxiv.org/abs/1602.01431
made a significant impact in the field, coming up with a heuristic argument for why ranks of elliptic curves should be bounded. The same heuristic suggests, albeit more loosely, that we should perhaps be a little bit surprised to see a curve with rank at least 30. So it's mild evidence that the heuristic itself could be mistaken.