curve #6376

y² + xy + y = x³ − 26975424619888x + 248158784903123874162

a-invariants: [1, 0, 1, -26975424619888, 248158784903123874162]
c-invariants: [1294820381754601, -214409192098529599908085]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 1810534797820489805011688523163678338628622
discriminant (Δ): -25347487169486857270163639324291496740800708
Faltings height: 7.0103
naive height: 107.4443
primes of bad reduction: 2, 7, 823, 6269, 9341, 71537, 3882145877, 9662395040672131
regulator: 14199640123216.19345250387880248551765547613230795871342255143750654075
submitted by: apkorte
submitted at: 2026-11-01 20:50:51 UTC
last updated: 2026-11-01 20:50:51 UTC

Witness: 16 independent points log in to add more points →

(2766049, -13955112143)
(5249425, -15852195947)
(-3018303, -17378985379)
(6050001, 17501336825)
(-4903025, 16205937153)
(4049898, -14331581005)
(10309291, 32640641775)
(4647474, 14936620818)
(5904226, -17170084302)
(16269819, -64164262603)
(10292358, -32575296145)
(19239121, 82757622325)
(12486928, 43102021921)
(2016415, -14212402799)
(3120705, -13943165919)
(663551, -15184250127)

Commentary

From the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public, file submission/board/1-16-m10-194825.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 2026-11-01 20:50:51 UTC · history