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curve #4526

y² + xy = x³ − x² − 137541786x + 2236782573008

a-invariants: [1, -1, 0, -137541786, 2236782573008]
c-invariants: [6602005737, -1932550434053109]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 116627545428822
discriminant (Δ): -1994787610407759765964928076
Faltings height: 3.9216
naive height: 70.3952
primes of bad reduction: 2, 3, 67, 73, 151, 521, 1871
regulator: 8650.3811395681754989406985544732177235496621841408
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:33:54 UTC
last updated: 2026-10-17 10:33:54 UTC

Witness: 6 independent points log in to add more points →

(-12376, -1423256)
(-16472, -173072)
(51238, -11414396)
(-1862341/121, 1129790339/1331)
(174214, 72478294)
(-9178, 1655638)

Commentary

BASE torsion/torsion_Z3.tsv.gz:556 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:33:54 UTC · history

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