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curve #4448

y² + xy = x³ − x² − 709x − 1391

a-invariants: [1, -1, 0, -709, -1391]
c-invariants: [34041, 1354995]
rank (lower bound): ≥ 6
torsion subgroup: trivial
conductor (N): 10882623866
discriminant (Δ): 21765247732
Faltings height: 0.6742
naive height: 31.3060
primes of bad reduction: 2, 24859, 218887
regulator: 130.18893175925852872949372731408328686657076258272
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:24:23 UTC
last updated: 2026-10-17 10:24:23 UTC

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

(-25, 28)
(-24, 49)
(-10, 73)
(-8, 65)
(-7, 60)
(-2, 5)

Commentary

BASE records/rank_6.md#15 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:24:23 UTC · history

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