curve #6384

y² + xy = x³ − x² − 16564271691739x + 41478778234822314169

a-invariants: [1, -1, 0, -16564271691739, 41478778234822314169]
c-invariants: [795085041203481, -35837660817003794026365]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 226191202571113654370827357711594425727714
discriminant (Δ): -452382405142227308741654715423188851455428
Faltings height: 6.6899
naive height: 103.8666
primes of bad reduction: 2, 1213, 7951, 36637, 320068736241973765083990670247
regulator: 46550821033198.00726183284043831128983850554971965180303450665075516083
submitted by: apkorte
submitted at: 2026-11-02 00:52:46 UTC
last updated: 2026-11-02 00:52:46 UTC

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

(2406828, -3945027043)
(1702388, 4266899005)
(2490336, 3957627275)
(2561548, 3980711895)
(1257512, -4758522845)
(926174, -5190053657)
(770748, -5401289305)
(745576, -5435748381)
(620430, -5607504797)
(3544270, 5222508207)
(-114152, -6585391693)
(3765480, -5702450333)
(-550940, -7101658657)
(-682544, -7243045221)
(-878178, 7440056603)
(-901084, -7460979651)

Commentary

From the Layr-Labs elliptic-rank-challenge-public repository (https://github.com/Layr-Labs/elliptic-rank-challenge-public, file submission/board/1-16-m10-004156.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 00:52:46 UTC · history