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curve #4328

y² + xy + y = x³ − 651058919645x + 202198826167124052

a-invariants: [1, 0, 1, -651058919645, 202198826167124052]
c-invariants: [31250828142937, -174699832684637395549]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 70344906853811702
discriminant (Δ): -15712229917480115978132451995116
Faltings height: 5.3179
naive height: 93.2192
primes of bad reduction: 2, 7, 41, 43, 61, 109, 113, 1663, 2281
regulator: 106144.6700355996243365635639936882725973789313756163
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:04 UTC
last updated: 2026-10-17 10:05:04 UTC

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

(554905, 108300428)
(11029257, -36538651590)
(29786329/64, 189384769/512)
(688401, -283610454)
(59436006/121, 39928062706/1331)
(6501955205/14161, 12954829424144/1685159)
(-49807307/144, 1073899628921/1728)

Commentary

BASE torsion/torsion_Z3.tsv.gz:4787 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:04 UTC · history

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