curve #5898

y² = x³ + x² − 16850701705x + 831538792987959

a-invariants: [0, 1, 0, -16850701705, 831538792987959]
c-invariants: [808833681856, -718454370143687680]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 316906423801103467072
discriminant (Δ): 7506920113560885578680918249472
Faltings height: 4.7291
naive height: 82.2566
primes of bad reduction: 2, 7, 17, 73, 137, 311, 4673, 20897
regulator: 377518.28984797835679045228543822775698292944707137366432
submitted by: The Wren
submitted at: 2026-10-25 20:29:40 UTC
last updated: 2026-10-25 20:29:40 UTC

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

(85417, 3926524)
(-101974, 38593859)
(28039, 19521952)
(100649, 12455492)
(-1453, 29257816)
(102791, 13621216)
(63079, -4427888)
(58727, 6670256)
(-6485, 30668272)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 1874th data row, added 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 316906423801103467072. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 20:29:40 UTC · history