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curve #4530

y² = x³ − 969842223x + 6582719885778

a-invariants: [0, 0, 0, -969842223, 6582719885778]
c-invariants: [46552426704, -5687469981312192]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 33192645983640
discriminant (Δ): 39663062906229094433315385600
Faltings height: 4.1861
naive height: 73.6915
primes of bad reduction: 2, 3, 5, 11, 13, 19, 181, 313, 599
regulator: 1081.0551899404491531078098965787361461015040566997
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:34:08 UTC
last updated: 2026-10-17 10:34:08 UTC

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

(37263, 4710024)
(110889/25, 192361662/125)
(-9687, 3881826)
(39141, 5346666)
(1581, 2247966)
(-4779, 3332934)

Commentary

BASE torsion/torsion_Z2xZ2.tsv.gz:64 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:34:08 UTC · history

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