curve #6377

y² + xy = x³ + x² − 29615877606802x + 83488020962854498960

a-invariants: [1, 1, 0, -29615877606802, 83488020962854498960]
c-invariants: [1421562125126521, -72133660773622225550285]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 224779804212575443651319563531863075014898
discriminant (Δ): -1348678825275452661907917381191178450089388
Faltings height: 6.7900
naive height: 105.2656
primes of bad reduction: 2, 3, 653, 5077, 7561, 1494536257407572062714658001163
regulator: 41646759737598.56385214407197366425732892888180203541636111846570647503
submitted by: apkorte
submitted at: 2026-11-01 20:51:18 UTC
last updated: 2026-11-01 20:51:18 UTC

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

(3095680, 4632390100)
(3247678, 4641629242)
(2102824, -5524588328)
(1923286, -5801178326)
(1547158, -6432803648)
(1153066, -7133039846)
(4700008, 6934271440)
(4768846, 7118505370)
(5138842, 8182888492)
(-1885778, -11515604774)
(3407413, 4703203612)
(-2332574, -11825834540)
(3544591, 4798909855)
(-3100454, 12064162234)
(4152529, -5668766096)
(219007, 8775563746)

Commentary

From the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public, file submission/board/1-16-m10-202013.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 20:51:18 UTC · history