curve #5906

y² + xy + y = x³ − 19481606373x + 1042696102197692

a-invariants: [1, 0, 1, -19481606373, 1042696102197692]
c-invariants: [935117105881, -900890834974464925]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 1846857170962581693626
discriminant (Δ): 3531971987408914035187943695172
Faltings height: 4.7150
naive height: 82.6918
primes of bad reduction: 2, 17, 19, 29, 31, 37, 89, 937, 9257, 111337
regulator: 346076.92111549084920037899879149738420560345479497307779
submitted by: The Wren
submitted at: 2026-10-25 21:02:22 UTC
last updated: 2026-10-25 21:02:22 UTC

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

(52625, -12801932)
(85894, -1789893)
(222455, 87737428)
(590665/9, 183843902/27)
(2493929/25, 1192731748/125)
(-119610, 40823611)
(1140943, -1210545360)
(-136102, -34182005)
(100429, -10005398)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 2279th 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 1846857170962581693626. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 21:02:22 UTC · history