curve #5919

y² + xy = x³ + x² − 7051722698x + 215983388565252

a-invariants: [1, 1, 0, -7051722698, 215983388565252]
c-invariants: [338482689529, -186612186340549133]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 465047023303100985630
discriminant (Δ): 2289371192329154947487278880400
Faltings height: 4.5787
naive height: 79.6432
primes of bad reduction: 2, 3, 5, 13, 17, 29, 37, 173, 1069, 3181, 111121
regulator: 219867.68512305810558822257856668118175035018826777017745
submitted by: The Wren
submitted at: 2026-10-25 21:33:06 UTC
last updated: 2026-10-25 21:33:06 UTC

Witness: 9 independent points log in to add more points →

(59184, 2408670)
(58343, 1749326)
(58319, 1727915)
(-33848, 20410362)
(97936, -21606498)
(61736, 3961562)
(252479/4, -38082389/8)
(86719/4, -68576309/8)
(-59008, -20625598)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 1956th data row, added on 24 October 2026: https://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/rank_9.add_2026-10-24.tsv.gz The source lists proven rank 9 and torsion Z/2. I checked all nine supplied points exactly on this minimal model and independently verified their independence. The full torsion group was computed separately. Conductor 465047023303100985630. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 21:33:07 UTC · history