Alpöge and Howell report elliptic curves over the rationals with at least 30 and at least 31 independent rational points of infinite order.
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Alpöge and Howell report elliptic curves over the rationals with at least 30 and at least 31 independent rational points of infinite order. Dujella’s specialist table records the rank-at-least-31 example as the current record, and the news account attributes assistance to an internal Claude model.
Read original source Original rank-at-least-31 record, point data and attributionelliptic-rank.icarm.cloud
Original report: 2026-08-23Alpöge and Howell report elliptic curves over the rationals with at least 30 and at least 31 independent rational points of infinite order. Dujella’s specialist table records the rank-at-least-31 example as the current record, and the news account attributes assistance to an internal Claude model.
Elkies and Klagsbrun’s 2024 construction had rank at least 29, improving the rank-at-least-28 record from 2006. The 2026 constructions raise this explicit lower-bound record to at least 31.
If correct, advances a concrete longstanding construction record in arithmetic geometry, with human expertise and AI-assisted search retained in the attribution.
A sourced advance or substantial formalization with the exact target, hypotheses, baseline and AI role stated. Importance and verification are assessed separately.
Background review: 2026-10-11. Selected sources:
Publication dates and editorial changes.
Alpöge–Howell–Claude: elliptic curves of rank at least 30 and 31
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