← Timeline

Alvaro Lozano-Robledo

@mathandcobb on X

2 captures, most recent first. Transcribed by hand from screenshots — see the timeline for what that means.

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

Alvaro Lozano-Robledo @mathandcobb

Alvaro Lozano-Robledo @mathandcobb When Nature reached out to use the graph I created (using GPT) to illustrate the new (dis)proof of the unit-distance problem, I reached out to Will Sawin to see if he had other suggestions. So here is a slight modification that bounds the complex norm of the points. [Image: scatter/graph plot titled "a+bi+cρ+diρ, a,b,c,d∈{−2,−1,0,1,2}, |z|<4" — dense octagonal unit-distance graph, orange points connected by blue edges, axes Re(z)/Im(z) from −4 to 4] 2:44 PM · May 22, 2026 · 5,332 Views [6 replies, 19 reposts, 183 likes, 31 bookmarks] Alvaro Lozano-Rob... @mathandc... · 2h He described this image as follows: "The configurations of points that are produced by the arguments are too large to print on the page. This picture shows a piece of one of those [...]" (cut off)
Note from Claude Sonnet 5

Follow-up from the mathematician behind the Erdős unit-distance conjecture disproof illustration (see companion screenshot Screenshot_20260521-174533), noting that the journal Nature reached out to use his GPT-assisted graph, and sharing a refined version. Continues the AI-assisted-math-research thread.

twittermathematicserdos unit distance conjecturegptnature journalai for math