curve #6420

y² + xy + y = x³ − x² − 11410853110239262870136397x + 14958076590579184569599875940861313525

a-invariants: [1, -1, 1, -11410853110239262870136397, 14958076590579184569599875940861313525]
c-invariants: [547720949291484617766547041, -12923778174257950723862481132124225424145]
rank (lower bound): ≥ 22
torsion subgroup: trivial
conductor (N): 1146006744764429998113223917296461852988673345797842574116735325482 ★ record for rank ≥ 22
discriminant (Δ): -1567547704826318075043522346343012995213105282208213977378156796038189088768 ★ record for rank ≥ 22
Faltings height: 13.2495 ★ record for rank ≥ 22
naive height: 184.7198 ★ record for rank ≥ 22
primes of bad reduction: 2, 13, 19, 83, 600033850919, 826463538148562116651, 56361518107158594265220078789
regulator: 212359061722724769691.1614869296190346621347154889664392626748147341723907536571472
submitted by: apkorte
submitted at: 2026-11-02 14:16:29 UTC
last updated: 2026-11-02 14:16:29 UTC

Witness: 22 independent points log in to add more points →

(-525062923441, -4561220771636967560)
(1568462846063, -958705524191296328)
(1926281784527, -353759570159311880)
(1302446082323, -1518381581075598088)
(-3821920653217, -1656005535105699848)
(-3028340725297, -4662784847877788936)
(2231185392835, 778207554027319684)
(1465705064105, 1175538670970454890)
(2112680878713, 529497337239145772)
(3292316324865, -3616145584049368180)
(-3203431131889, -4317224504907381704)
(8645466325635, 23717150355200797880)
(1767772284411, 557321671977943896)
(15265393723263, -58293196680118075528)
(92734809048543/49, 128842137577401044616/343)
(23626373097895, 113726557413399357760)
(-3721504199623, -2425342230137476198)
(-150746324413697/81, 3976126064069346830456/729)
(18568302618727/9, 12006541991396809064/27)
(-32729855306405/9, 78066153741112083308/27)
(-91175713171331/25, -354993700131091293988/125)
(6525429003391/49, -1257497714459795271800/343)

Commentary

From the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public, file submission/board/1-22-m10-103424.ec), where it is recorded as a find of that challenge; not our discovery. Posted by apkorte with Claude (Anthropic), which moved the points to the minimal model and checked their independence.

last edited by apkorte at 2026-11-02 14:16:29 UTC · history