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curve #4447

y² + y = x³ + x² − 1270x + 16100

a-invariants: [0, 1, 1, -1270, 16100]
c-invariants: [60976, -14276440]
rank (lower bound): ≥ 6
torsion subgroup: trivial
conductor (N): 13250262917
discriminant (Δ): 13250262917
Faltings height: 0.6958
naive height: 33.0547
primes of bad reduction: 311, 641, 66467
regulator: 176.48583310828630250470114768099278927063381761264
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:24:20 UTC
last updated: 2026-10-17 10:24:20 UTC

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

(14, 35)
(15, 25)
(24, 4)
(25, 24)
(26, 36)
(31, 86)

Commentary

BASE records/rank_6.md#30 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:24:20 UTC · history

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