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curve #4332

y² = x³ + x² − 19174046905x + 4622529185724528

a-invariants: [0, 1, 0, -19174046905, 4622529185724528]
c-invariants: [920354251456, -3993870738591500896]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 488419260057789580
discriminant (Δ): -8779754406754739330591804097742000
Faltings height: 5.1951
naive height: 85.6626
primes of bad reduction: 2, 5, 13, 17, 19, 31, 103, 1821453097
regulator: 14280.05728218940979970000488122336179317471425070914
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:12 UTC
last updated: 2026-10-17 10:05:12 UTC

Witness: 7 independent points log in to add more points →

(-120484, 71998030)
(461981, 307186685)
(4331691, 9011074995)
(3635801/16, 7010662555/64)
(139797, 68367795)
(52247, 61346285)
(-9984061/49, 2872279115/343)

Commentary

BASE torsion/torsion_Z3.tsv.gz:4895 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:13 UTC · history

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