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curve #4331

y² = x³ + x² − 45497850737x + 3791453321455816

a-invariants: [0, 1, 0, -45497850737, 3791453321455816]
c-invariants: [2183896835392, -3275828773118837344]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 97496466025975564
discriminant (Δ): -182387047474083046526684049136816
Faltings height: 4.9878
naive height: 85.2662
primes of bad reduction: 2, 17, 19, 23, 41, 71, 109, 10340221
regulator: 11595.75804659319308821360191863779387481452793219767
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:10 UTC
last updated: 2026-10-17 10:05:10 UTC

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

(143587, 14796613)
(119092, 7880858)
(171348, 32036194)
(1142983, 1202079061)
(113871, 9332779)
(1847503/9, 1503785609/27)
(1934637/4, 2464815907/8)

Commentary

BASE torsion/torsion_Z3.tsv.gz:4799 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

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

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