Alvaro Lozano-Robledo @mathandcobb
— saved image
Alvaro Lozano-Robledo @mathandcobb [siren emoji] RANK 31 [siren emoji] Ava Howell has submitted an elliptic curve of rank 31! elliptic-rank.icarm.cloud/curve/302 [embedded card] curve #302 y^2 + xy + y = x^3 + x^2 − 1284727764113567728281797636015784768866707681415849262157224232063x + 56036832145426133925685933890191531233276985868494540685804386919945671068198905886330[cut off] a-invariants [1, 1, 1, -1284727764113567728281797636015784768866707681415849262157224232063, 56036832145426133925685933890191531233276985868494540685804386919945671068 1989058863306170127006181] rank (lower bound) ≥ 31 torsion subgroup trivial naive height 468.2771 [badge: record for rank ≥ 31] Faltings height 36.7425 [badge: record for rank ≥ 31] 1:07 PM · Aug 23, 2026 · 78.6K Views 23 replies · 98 reposts · 799 likes · 122 bookmarks Relevant ▾ · View quotes > [reply] Alvaro Lozano-R... @mathan... · Aug 23 BSD + GRH certified to rank 31, found by Claude, Levent Alpöge, and Ava Howell.
Note from Claude Sonnet 5
Tweet by arithmetic geometer Alvaro Lozano-Robledo announcing an elliptic curve of rank 31 submitted by Ava Howell to a rank-records site, with a card showing the curve's Weierstrass coefficients and heights; his reply credits the BSD + GRH-certified result to Claude, Levent Alpöge, and Ava Howell. The very long integer coefficients were transcribed as read from a small rendering and may contain digit errors.
elliptic curvesrank recordai for mathclaudenumber theorybsd conjecture