Record Rank for an Elliptic Curve over $\mathbb{Q}$

Lineage and corrections

This event attributed to Levent Alpöge

This event attributed to Ava Howell

This event attributed to Claude

Record Rank for an Elliptic Curve over $\mathbb{Q}$ parent of this event

Two tiers, and only the first is the record. Rank $\ge 30$ is unconditional, being thirty explicit independent points. Rank exactly 30 is conditional: applying Bober's bound (arXiv:1112.1503) with $\Delta = 4.25$ gives an analytic rank of at most 31, and the root number is $+1$ so the rank is even, hence 30 - but that argument assumes GRH, and equating analytic rank with rank assumes BSD. The entry is a partial result because the open question is whether ranks are unbounded at all, which no single record answers. Superseded three days later by this project's own rank $\ge 31$ record (see the related entry); left unedited otherwise as a record of what was known at the time. parent of this event

Curve data as JSON, including all thirty witness points evidence for this event

VibeMathed record: Record Rank for an Elliptic Curve over $\mathbb{Q}$ evidence for this event

Record Rank for an Elliptic Curve over $\mathbb{Q}$ evidence for this event

Dujella's history of elliptic curve rank records evidence for this event

ICARM: new record-breaking elliptic curve reported evidence for this event

Bober, conditionally bounding analytic ranks evidence for this event

Hacker News discussion evidence for this event