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curve #4493

y² + xy = x³ − x² − 3946x + 143896

a-invariants: [1, -1, 0, -3946, 143896]
c-invariants: [189417, -123473781]
rank (lower bound): ≥ 7
torsion subgroup: trivial
conductor (N): 2444942116858
discriminant (Δ): -4889884233716
Faltings height: 1.1346
naive height: 37.2631
primes of bad reduction: 2, 212881, 5742509
regulator: 10569.24386680611867504988034227441439188827486912913
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:31:23 UTC
last updated: 2026-10-17 10:31:23 UTC

Witness: 7 independent points log in to add more points →

(-76, 60)
(-70, 306)
(-66, 370)
(-55, 466)
(-14, 450)
(230, 3256)
(340, 5996)

Commentary

BASE records/rank_7.md#20 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:31:23 UTC · history

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