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curve #4490

y² + y = x³ − 28399x + 454320

a-invariants: [0, 0, 1, -28399, 454320]
c-invariants: [1363152, -392532696]
rank (lower bound): ≥ 8
torsion subgroup: trivial
conductor (N): 1376680825642789
discriminant (Δ): 1376680825642789
Faltings height: 1.5958
naive height: 42.3759
primes of bad reduction: 479, 857, 5503, 609421
regulator: 15647.0968537404311237802721875620644502862360076293537
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:31:15 UTC
last updated: 2026-10-17 10:31:15 UTC

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

(-14, -922)
(-87, 1505)
(-75, -1471)
(-3, 734)
(232, 2520)
(-118, -1471)
(-168, -696)
(-172, -501)

Commentary

BASE records/rank_8.md#20 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:31:15 UTC · history

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