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curve #4351

y² + xy = x³ − x² − 593095836x + 5559644322516

a-invariants: [1, -1, 0, -593095836, 5559644322516]
c-invariants: [28468600137, -4803404585953221]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
conductor (N): 230626081062
discriminant (Δ): 20465260742358948204
Faltings height: 3.4374
naive height: 72.2162
primes of bad reduction: 2, 3, 13, 31, 37, 43, 6661
regulator: 5808.88947170441240455399530559635345677631026053
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:54 UTC
last updated: 2026-10-17 10:05:54 UTC

Witness: 5 independent points log in to add more points →

(-3641/4, 19760167/8)
(94009, 27892560)
(13981, 9380)
(1963096/121, 595500514/1331)
(613998202/43681, -55990717632/9129329)

Commentary

BASE torsion/torsion_Z3.tsv.gz:131 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:54 UTC · history

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