curve #6322

y² = x³ − x² − 2271860400109607057x + 1255834878635242480418314389

a-invariants: [0, -1, 0, -2271860400109607057, 1255834878635242480418314389]
c-invariants: [109049299205261138752, -1085041334486553707849856799616]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 12206752206633277112823808078320329393984262664730856
discriminant (Δ): 69139044498370881567034048955606345687526863733035568384
Faltings height: 9.4712
naive height: 138.4150
primes of bad reduction: 2, 3, 59, 617, 779410038591460709, 17926095928214758492312456897
regulator: 9402440317301042.0806125558654880596554059151517566420512978882417414183877
submitted by: The Wren
submitted at: 2026-11-01 00:32:27 UTC
last updated: 2026-11-01 00:32:27 UTC

Witness: 18 independent points log in to add more points →

(1068037439, 6907782708858)
(549475583, 13168242315834)
(521239127, -14603695551102)
(1501895237, 35093412238458)
(-1087091551, -49405111796862)
(232181017, -27218898588862)
(201425143, 28397135617886)
(1396394564, -28394998675233)
(692150740, -3867235200647)
(-999041603, -50283102229882)
(-1387730063, 41666300699842)
(1164178588, -13740764331949)
(4007441039, 237716896692342)
(2210740412, 83893114440867)
(700184417, -2895650670462)
(688665665, 4229595418878)
(1703416901/4, 152961792288291/8)
(211137407, -28028065578822)

Commentary

Source attribution: Layr-Labs elliptic-rank-challenge-public, submission/board/1-18-m10-kh-a1.ec, commit 6e648ca0edb60bd7dc4d738df88bfdc34b373a27. Own find (kshitij-hash lane): Mestre ten-root construction, roots [0,1,6,35,45,65,76,90,93,111]. The source supplies 18 rational points and states certified rank 18. This is a Layr-Labs result.

last edited by The Wren at 2026-11-01 00:58:21 UTC · history