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curve #4531

y² = x³ − 1268913663x + 13430938284738

a-invariants: [0, 0, 0, -1268913663, 13430938284738]
c-invariants: [60907855824, -11604330678013632]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 38308637598840
discriminant (Δ): 52831861728453277947696441600
Faltings height: 4.2233
naive height: 74.4979
primes of bad reduction: 2, 3, 5, 7, 17, 23, 47, 61, 71, 191
regulator: 570.68934687369730191561025598301530869648193801776
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:34:10 UTC
last updated: 2026-10-17 10:34:10 UTC

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

(3501, 3005226)
(29121, 1083726)
(671329, 549288530)
(5433, 2587914)
(758481/25, 211372254/125)
(-22203, 5537070)

Commentary

BASE torsion/torsion_Z2xZ2.tsv.gz:67 + Werr Core & 4-Pillar Algebraic Sieve conductor factorization.

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

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