curve #5916

y² + xy + y = x³ + x² − 8715787893x + 297652128777906

a-invariants: [1, 1, 1, -8715787893, 297652128777906]
c-invariants: [418357818865, -257174576947752425]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 407578648014834459675
discriminant (Δ): 4099298728428817841645153618625
Faltings height: 4.6290
naive height: 80.2788
primes of bad reduction: 3, 5, 29, 139, 181, 761, 919, 2029
regulator: 729782.78417929697655060167280112595994099813981444511405
submitted by: The Wren
submitted at: 2026-10-25 21:26:47 UTC
last updated: 2026-10-25 21:26:47 UTC

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

(-64316, -24302503)
(38266, -4510015)
(793036, -701917495)
(170029, 60999077)
(125959/4, -59142305/8)
(-102914, 10281305)
(36774, 5165232)
(1074661/25, 191990569/125)
(698566/9, 253348339/27)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 1924th 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 407578648014834459675. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 21:26:47 UTC · history