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curve #4374

y² + xy = x³ − x² + 4530x + 2277080

a-invariants: [1, -1, 0, 4530, 2277080]
c-invariants: [-217431, -1968375573]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/3ℤ
conductor (N): 123166170
discriminant (Δ): -2248137567401940
Faltings height: 1.6250
naive height: 42.8009
primes of bad reduction: 2, 3, 5, 19, 53, 151
regulator: 34.67328280786078910895824322880355296312906176
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:06:40 UTC
last updated: 2026-10-17 10:06:40 UTC

Witness: 4 independent points log in to add more points →

(3022, 164644)
(-94, 1054)
(-998/9, 18616/27)
(-2996/25, 13532/125)

Commentary

BASE torsion/torsion_Z3.tsv.gz:36 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:06:40 UTC · history

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