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curve #4373

y² + xy = x³ − x² − 26196x + 2031596

a-invariants: [1, -1, 0, -26196, 2031596]
c-invariants: [1257417, -1749640581]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/3ℤ
conductor (N): 69812118
discriminant (Δ): -621031986443916
Faltings height: 1.5519
naive height: 42.5654
primes of bad reduction: 2, 3, 19, 37, 613
regulator: 19.20116789751017954265081275051284399506030097
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:06:38 UTC
last updated: 2026-10-17 10:06:38 UTC

Witness: 4 independent points log in to add more points →

(740, 19314)
(-185, 814)
(2146, 98050)
(-148, 1702)

Commentary

BASE torsion/torsion_Z3.tsv.gz:17 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:06:38 UTC · history

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