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curve #4376

y² = x³ + x² − 51837x + 5033791

a-invariants: [0, 1, 0, -51837, 5033791]
c-invariants: [2488192, -4364124544]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/3ℤ
conductor (N): 67767916
discriminant (Δ): -2107024864258816
Faltings height: 1.6723
naive height: 44.3934
primes of bad reduction: 2, 17, 41, 109, 223
regulator: 43.65124063445715591666735046554949687232348869
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:06:43 UTC
last updated: 2026-10-17 10:06:43 UTC

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

(762, 20213)
(-263, 738)
(2853, 151946)
(-54, 2771)

Commentary

BASE torsion/torsion_Z3.tsv.gz:15 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:06:44 UTC · history

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