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curve #4529

y² = x³ − x² − 1598016096x + 23734429258320

a-invariants: [0, -1, 0, -1598016096, 23734429258320]
c-invariants: [76704772624, -20506086650552768]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 66755917890480
discriminant (Δ): 17825410293602030933098521600
Faltings height: 4.1877
naive height: 75.1897
primes of bad reduction: 2, 3, 5, 7, 13, 17, 29, 37, 41, 61, 67
regulator: 491.81979072140901140161860149459215430108263712527
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:34:05 UTC
last updated: 2026-10-17 10:34:05 UTC

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

(-962, 5027010)
(3662424/25, 6770377068/125)
(1097838, 1149537090)
(2120, 4511780)
(32904, 2603172)
(26549, 145058)

Commentary

BASE torsion/torsion_Z2xZ2.tsv.gz:78 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:34:05 UTC · history

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