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curve #4327

y² = x³ + x² − 5128777269002x + 4470629773280671441

a-invariants: [0, 1, 0, -5128777269002, 4470629773280671441]
c-invariants: [246181308912112, -3862625601202353597664]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 149257164040100036
discriminant (Δ): 861440132820936499661781814544
Faltings height: 5.6568
naive height: 99.4113
primes of bad reduction: 2, 19, 109, 127, 191, 331, 811, 2767
regulator: 116887.6775617209820304694295123300341052042943518618
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:02 UTC
last updated: 2026-10-17 10:05:02 UTC

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

(106921, -1980777151)
(981092, -619007403)
(522046801/400, -37959089599/8000)
(2531319121/1936, 1980777151/85184)
(20919033/16, 9322901/64)
(5364549/4, 535024097/8)
(64083364/49, -210710627/343)

Commentary

BASE torsion/torsion_Z3.tsv.gz:4821 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:03 UTC · history

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