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curve #4431

y² + xy = x³ − x² − 113014x + 14706784

a-invariants: [1, -1, 0, -113014, 14706784]
c-invariants: [5424681, -12682250325]
rank (lower bound): ≥ 8
torsion subgroup: trivial
conductor (N): 349101890324014
discriminant (Δ): -698203780648028
Faltings height: 1.7014
naive height: 46.5269
primes of bad reduction: 2, 1741, 66103, 1516709
regulator: 59931.2880104292363607190590611830478880825348505382772
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:23:38 UTC
last updated: 2026-10-17 10:23:38 UTC

Witness: 8 independent points log in to add more points →

(-358, 3210)
(-338, 3938)
(-240, 5408)
(-206, 5508)
(-154, 5410)
(130, 1418)
(291, 2384)
(618, 13130)

Commentary

BASE records/rank_8.md#36 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:23:38 UTC · history

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