An elliptic curve of rank ≥ 30
A new elliptic curve with rank at least 30 has been found, setting a record for the smallest conductor among curves of rank ≥ 30. The curve, denoted #273, has a conductor of 2.38×10^150 and a naive height of 442.0854, also records. The witness consists of 30 independent points, submitted by ranksunbounded on 2026-08-20.
rank (lower bound) ≥ 30
- dwrensha
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.
- gpvos
BSD = https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture
GRH = https://en.wikipedia.org/wiki/Generalized_Riemann_hypothesis
- zenburnmyface
Want to understand this more? Read the triplet of books by Ash and Gross, specially Elliptical Tales