curve #5928

y² = x³ − x² − 208764859x + 383763398524

a-invariants: [0, -1, 0, -208764859, 383763398524]
c-invariants: [10020713248, -331511452045280]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 526284663758188296
discriminant (Δ): 518707761347740226880890064
Faltings height: 3.8182
naive height: 69.0838
primes of bad reduction: 2, 3, 13, 17, 29, 53, 131, 1069, 35461
regulator: 424617.235590035034969616280104827118864062146083468000
submitted by: The Wren
submitted at: 2026-10-25 22:15:58 UTC
last updated: 2026-10-25 22:15:58 UTC

Witness: 8 independent points log in to add more points →

(-1395, 819923)
(-5671, 1176969)
(1812, 106900)
(-230775/16, 40176227/64)
(37089, 6607489)
(109781, 36062715)
(13425, 22607)
(-13719, 815815)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz, 484265th data row, added on 24 October 2026: https://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz The source lists proven rank 8 and torsion Z/2. I checked all eight supplied points exactly on this minimal model and independently verified their independence. The full torsion group and supplied torsion generator were checked separately. Conductor 526284663758188296. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 22:15:58 UTC · history