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curve #4433

y² + y = x³ − 22477x + 1920276

a-invariants: [0, 0, 1, -22477, 1920276]
c-invariants: [1078896, -1659118680]
rank (lower bound): ≥ 8
torsion subgroup: trivial
conductor (N): 866216414066363
discriminant (Δ): -866216414066363
Faltings height: 1.5666
naive height: 42.4591
primes of bad reduction: 251879, 3439017997
regulator: 282847.055367482657870173003410388392858173985995574428
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:23:44 UTC
last updated: 2026-10-17 10:23:44 UTC

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

(-727/4, 327/8)
(-178, 530)
(-176, 651)
(-174, 750)
(-169, 944)
(-163, 1119)
(-559/4, 12213/8)
(-123, 1680)

Commentary

BASE records/rank_8.md#27 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:23:44 UTC · history

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