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curve #4329

y² + xy + y = x³ − 1053728083560x + 416333248953396002

a-invariants: [1, 0, 1, -1053728083560, 416333248953396002]
c-invariants: [50578948010857, -359712002964156162229]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 156061640559670622
discriminant (Δ): -83230850279057972347925564263516
Faltings height: 5.4435
naive height: 94.6637
primes of bad reduction: 2, 7, 19, 223, 367, 439, 797, 2927
regulator: 130843.1032446517784392477929200026665129330094442310
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:06 UTC
last updated: 2026-10-17 10:05:06 UTC

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

(589461, 3990397)
(302005, 354316341)
(9486989/16, -57923599/64)
(5340175/9, -36223279/27)
(622399, -40302269)
(18989092690/32041, -4458933110631/5735339)
(6320517604/10609, -4894395034173/1092727)

Commentary

BASE torsion/torsion_Z3.tsv.gz:4823 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:06 UTC · history

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