curve #5921

y² + xy = x³ + x² − 3943808908x + 80223947186812

a-invariants: [1, 1, 0, -3943808908, 80223947186812]
c-invariants: [189302827609, -69314910140612573]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 406419341000678787990
discriminant (Δ): 1145379728888137884914147664900
Faltings height: 4.4886
naive height: 77.8998
primes of bad reduction: 2, 3, 5, 13, 23, 41, 79, 97, 10009, 14408161
regulator: 209440.30833555227133682212336792063290597000231485262495
submitted by: The Wren
submitted at: 2026-10-25 21:36:55 UTC
last updated: 2026-10-25 21:36:55 UTC

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

(234, 8905000)
(18473, 3688646)
(9646, -6568328)
(-52143, 12030161)
(17212, 4167826)
(1498, 8620126)
(137254/9, -131444456/27)
(246714, -118968824)
(51961, -3975023)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 1920th 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 406419341000678787990. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 21:36:55 UTC · history