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curve #4330

y² + y = x³ + x² − 14128811261x + 2214337813098111

a-invariants: [0, 1, 1, -14128811261, 2214337813098111]
c-invariants: [678182940544, -1913191939614411352]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 230025338628348235
discriminant (Δ): -1937722970604152246410595469045115
Faltings height: 5.0708
naive height: 84.1906
primes of bad reduction: 5, 7, 19, 31, 107, 113, 197, 373, 661
regulator: 60143.57421876942075028559159121255608673516106980418
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:08 UTC
last updated: 2026-10-17 10:05:08 UTC

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

(939499, 904542908)
(131391, 51246828)
(13881829/100, 54112105083/1000)
(1884361/25, 4964904159/125)
(3083929/16, 5219736987/64)
(-119561, 46845516)
(586541/4, 459252503/8)

Commentary

BASE torsion/torsion_Z3.tsv.gz:4839 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:08 UTC · history

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