Claude-assisted search breaks the elliptic curve rank record
Rank 30, then 31
Result confirmed
The takeaway
An elliptic curve over Q with rank at least 30 was reported on 20 Aug 2026 and one with rank ≥31 on 23 Aug. These broke the Elkies–Klagsbrun rank-29 record from 2024.
Status
- Claim
Result confirmed
- Our reporting
- Medium confidence
- Verification
- Expert-checked
- Importance
- 3 of 5
- Last verified
- 29 September 2026
Your AI and this story
- GPT-6 Astra115 days after its cutoff
- Claude Opus 5.554 days after its cutoff
- Gemini 4 Hydrogen145 days after its cutoff
- Grok 4.784 days after its cutoff
None of these four assistants can know about it. The closest, Claude Opus 5.5, stops 54 days before it.
Key facts
- Previous record: rank ≥ 29 (Elkies–Klagsbrun, 2024); earlier ≥ 28 (Elkies, 2006)
- Rank 30 on 20 Aug; rank 31 on 23 Aug 2026; first submitted under the name ‘ranksunbounded’
- 31 independent rational points given explicitly
What happened
AI-directed searches through families of elliptic curves found new record-rank examples twice in one week.
Why it matters
Rank records move very rarely (2006, 2024). Two in a week signal AI’s strength at large, structured searches in number theory.
Sources
3 sources from 3 sites. Numbers match the chips in the text.
3 sources: 3 primary
Primary
- ICARM: new record-breaking elliptic curve reportedicarm.io, official
- Andrej Dujella: history of elliptic curve rank recordsweb.math.pmf.unizg.hr, docs
- Epoch AI open problems: elliptic curve rankepoch.ai, official
Changes
- Filed