curve #5901

y² = x³ + x² − 66725156105x + 6632896258588279

a-invariants: [0, 1, 0, -66725156105, 6632896258588279]
c-invariants: [3202807493056, -5730841584265231360]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 586117568885134967872
discriminant (Δ): 6815169115215821516744666550272
Faltings height: 4.9130
naive height: 86.3851
primes of bad reduction: 2, 17, 19, 43, 103, 127, 179, 523, 1667
regulator: 406751.32644070703842854357020080022160131609807015886617
submitted by: The Wren
submitted at: 2026-10-25 20:47:18 UTC
last updated: 2026-10-25 20:47:18 UTC

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

(14427, -75321016)
(182935, 23420552)
(-296945, 16222352)
(151005, 616352)
(146041, 1751476)
(150771, 104576)
(150799, -229072)
(1593679/9, 519262552/27)
(3879541/36, 5689364959/216)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 2010th 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 586117568885134967872. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 20:47:18 UTC · history