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curve #4378

y² + xy = x³ − 87135479x + 313062038064

a-invariants: [1, 0, 0, -87135479, 313062038064]
c-invariants: [4182502993, -270491874641785]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 532725963
discriminant (Δ): 32532353639337135969
Faltings height: 3.0848
naive height: 66.4625
primes of bad reduction: 3, 7, 11, 37, 157, 397
regulator: 57.28862439650102662097489732204084968734124771
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:06:50 UTC
last updated: 2026-10-17 10:06:50 UTC

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

(4303, 131251)
(2125, 369742)
(5245, 15637)
(-416, 591172)

Commentary

BASE torsion/torsion_Z4.tsv.gz:25 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:06:50 UTC · history

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