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curve #4434

y² + xy + y = x³ + 21882x + 1502972

a-invariants: [1, 0, 1, 21882, 1502972]
c-invariants: [-1050359, -1296992485]
rank (lower bound): ≥ 8
torsion subgroup: trivial
conductor (N): 822049277971034
discriminant (Δ): -1644098555942068
Faltings height: 1.6053
naive height: 41.9666
primes of bad reduction: 2, 91099, 4511845783
regulator: 16144.6785586217097566096381471598834180710003895315591
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:23:46 UTC
last updated: 2026-10-17 10:23:46 UTC

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

(-59, 115)
(-57, 295)
(-1, 1217)
(11, 1315)
(22, 1401)
(64, 1747)
(83, 1931)
(197, 3571)

Commentary

BASE records/rank_8.md#14 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:23:46 UTC · history

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