curve #5905

y² = x³ − x² − 322904120339x + 70625095994257203

a-invariants: [0, -1, 0, -322904120339, 70625095994257203]
c-invariants: [15499397776288, -61019989942651565696]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 4008101126068867285632
discriminant (Δ): 1036760632192651681001330602752
Faltings height: 5.1285
naive height: 91.1155
primes of bad reduction: 2, 3, 17, 47, 83, 89, 263, 337, 1907, 10463
regulator: 5939547.1966941504784579998256465225335968787391927712562
submitted by: The Wren
submitted at: 2026-10-25 20:58:31 UTC
last updated: 2026-10-25 20:58:31 UTC

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

(327946, 7627)
(324402, 3637377)
(2966242/9, 40185611/27)
(3079978, 5319169477)
(325842, 2211567)
(446559, 124417410)
(17699137/121, 216762347668/1331)
(15983353/49, 639854804/343)
(330559, 2461390)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 2511th 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 4008101126068867285632. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 20:58:31 UTC · history