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curve #4334

y² + y = x³ − 14473553544x + 670209954121532

a-invariants: [0, 0, 1, -14473553544, 670209954121532]
c-invariants: [694730570112, -579061400361003864]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/3ℤ
conductor (N): 102112969676139
discriminant (Δ): -1832911113177429121881531
Faltings height: 4.2700
naive height: 81.8004
primes of bad reduction: 3, 17, 37, 71, 2287, 12343
regulator: 5674.1822277747415456785509932237582340639381539386
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:17 UTC
last updated: 2026-10-17 10:05:17 UTC

Witness: 6 independent points log in to add more points →

(411225/4, 131163479/8)
(69460, 1868)
(-32076, 33188275)
(69492, -15284)
(1112137/16, -1459941/64)
(295353/4, 16160519/8)

Commentary

BASE torsion/torsion_Z3.tsv.gz:547 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

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

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