curve #6324

y² + xy = x³ − x² − 1573007034494234315364x + 22388069790509695333386102725264

a-invariants: [1, -1, 0, -1573007034494234315364, 22388069790509695333386102725264]
c-invariants: [75504337655723247137481, -19343292298660607248594838142509445]
rank (lower bound): ≥ 19
torsion subgroup: trivial
conductor (N): 546321491073191762170183455262948859623343119820126508531642
discriminant (Δ): 32569502011819400093537656868955959215305223431196661932622369472
Faltings height: 11.1240
naive height: 158.0354
primes of bad reduction: 2, 3, 23, 1319617128196115367560829602084417535322084830483397363603
regulator: 638955495209250275.1260859313699026557841471703638317064654152771169677031358
submitted by: The Wren
submitted at: 2026-11-01 00:44:24 UTC
last updated: 2026-11-01 00:44:24 UTC

Witness: 19 independent points log in to add more points →

(17845269088, 15046999892620)
(17833573312, -86367780976652)
(28069188976, 591740136070924)
(-5080222688, 5499837270576340)
(58851566128, -11560606567717820)
(-44943439232, 1517451488370892)
(17814310651, 139272536479774)
(30036943603, 1496519919580567)
(9890948191, 2792337912684655)
(9507438325, 2879612048733808)
(9424644535, -2898309657448598)
(8083444201, -3193895739539501)
(-1539165803, 4980517017303643)
(16858241320, -813061227007388)
(156700233184, 60196814768338828)
(63734692057, 13454719810659955)
(27635657537, -152181027628452)
(-13901283872, 6447372604151692)
(2161649383, -4358656940680358)

Commentary

Source attribution: Layr-Labs elliptic-rank-challenge-public, submission/board/1-19-m10-kh-b1.ec, commit 587264a497665705f4236787ba4c1a395556957d. Own find from the kshitij-hash lane: Mestre ten-root construction, roots [0,10,12,31,47,48,58,59,72,95]. The source supplies 19 rational points and states certified rank 19. This is a Layr-Labs source result.

last edited by The Wren at 2026-11-01 01:00:27 UTC · history