curve #5918

y² + xy = x³ + x² − 165946862x + 221504643503460

a-invariants: [1, 1, 0, -165946862, 221504643503460]
c-invariants: [7965449401, -191380071727859885]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 316790999539997571186
discriminant (Δ): -21195501423418514840722245735408
Faltings height: 4.6898
naive height: 79.5861
primes of bad reduction: 2, 3, 13, 23, 29, 139, 173, 199, 257, 571
regulator: 461394.76673396348683503982819402435820696239161532808541
submitted by: The Wren
submitted at: 2026-10-25 21:31:08 UTC
last updated: 2026-10-25 21:31:08 UTC

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

(3632, -14866198)
(-9017, 14913162)
(250736, -126392470)
(81472, -27404554)
(104824, 36770634)
(-663499/25, 1801032811/125)
(694205/16, -1102457365/64)
(31293, -15730500)
(322096/25, -1861187634/125)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 1873rd 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 316790999539997571186. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 21:31:08 UTC · history