curve #6432

y² + xy = x³ − 427875600804034080080437x + 120105679085213644774350854276306081

a-invariants: [1, 0, 0, -427875600804034080080437, 120105679085213644774350854276306081]
c-invariants: [20538028838593635843860977, -103771306729655396128297028548494245449]
rank (lower bound): ≥ 21
torsion subgroup: trivial
conductor (N): 918058808899073726623099528906265241268897541825990815343615961414
discriminant (Δ): -1218359517525196338896421877209620226748919003347439715005774116856365056
Faltings height: 12.5632 ★ record for rank ≥ 21
naive height: 175.0705 ★ record for rank ≥ 21
primes of bad reduction: 2, 3, 3347, 708185867, 64552978246316524023424151593219593440610358630571281
regulator: 1753511819515244651727.6042236932564793580156926698668550416854877062700619850148
submitted by: apkorte
submitted at: 2026-11-03 00:37:35 UTC
last updated: 2026-11-03 00:37:35 UTC

Witness: 21 independent points log in to add more points →

(400656228434, -113974589214399721)
(-724481774254, -223230956719425385)
(-33530077678, -366626065895108905)
(-245934339406, 458759279480658167)
(196529795930, 208820718915424871)
(1419432058706, 1540330137083344919)
(1921272078770, 2527845104773833719)
(-20465088118, 358961874188103623)
(1619651453066, 1917257845433377199)
(2165797469810, 3058180370647982039)
(-730095024634, -208150039075132465)
(1904849026394, 2493333431841662567)
(894972821206, 673810141486171375)
(4771875836434, 10331394516470848279)
(-734815849502/9, 10612609861215480941/27)
(4091186155430, -8176007157498597301)
(13914352391186/25, -29147770105480285349/125)
(8603995484386/9, -20647127749190919827/27)
(4424232162526/9, 4563052504816732193/27)
(37731911349026, 231738604568522857895)
(-6055657312076/9, 8681404567302821693/27)

Commentary

From the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public, file submission/board/1-21-m10-003423.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 2026-11-03 00:37:35 UTC · history