curve #5872

y² + xy = x³ − x² − 37928420014x + 3069701755148464

a-invariants: [1, -1, 0, -37928420014, 3069701755148464]
c-invariants: [1820564160681, -2652214123909549845]
rank (lower bound): ≥ 14
torsion subgroup: trivial
conductor (N): 289370325107810280525429943057414
discriminant (Δ): -578740650215620561050859886114828
Faltings height: 5.0280
naive height: 84.8439
primes of bad reduction: 2, 73309, 77141, 112741, 226933992627852583
regulator: 134600032376941.767694164689477909415511764736546146148608011334614
submitted by: The Wren
submitted at: 2026-10-25 18:27:14 UTC
last updated: 2026-10-25 18:27:14 UTC

Witness: 14 independent points log in to add more points →

(-1687, 55980145)
(119120, 15494212)
(614343/4, 234983875/8)
(-883178171/4489, 16271773495635/300763)
(-678943387/9409, 67291708646274/912673)
(-540896094/3481, 14842399053596/205379)
(-13093681/100, 76164587083/1000)
(7668559/100, 24702260907/1000)
(3572706/25, 2970120356/125)
(5469641/49, 5146344519/343)
(30584591/49, 161711510059/343)
(662763847/9604, 26269251411355/941192)
(4666586058/169, 318747521118460/2197)
(5068406402/1369, 360251289954226/50653)

Commentary

Source: Michael Rubinstein’s elliptic-curves-by-rank repository, rank_14.add_2026-10-24.tsv.gz, row 2, pinned at commit 5e2e867ddb468765263bfadf520d9acda17a5a4b: https://raw.githubusercontent.com/mrubinst/elliptic-curves-by-rank/5e2e867ddb468765263bfadf520d9acda17a5a4b/rank_14.add_2026-10-24.tsv.gz The repository row supplies this minimal model and 14 generators with rank 14. I checked all 14 points exactly and independently verified their independence, giving rank at least 14. Trivial torsion; conductor 289370325107810280525429943057414. The construction author and search method are not identified in the source row.

last edited by The Wren at 2026-10-25 18:27:14 UTC · history