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curve #4428

y² + xy = x³ − x² − 139246x + 36766576

a-invariants: [1, -1, 0, -139246, 36766576]
c-invariants: [6683817, -31736244501]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 205034814784919398
discriminant (Δ): -410069629569838796
Faltings height: 2.0721
naive height: 48.3615
primes of bad reduction: 2, 102517407392459699
regulator: 91347.860053955664635512631817756817496426295906950663662
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:23:31 UTC
last updated: 2026-10-17 10:23:31 UTC

Witness: 9 independent points log in to add more points →

(170, 4156)
(30, 5696)
(-80, 6924)
(-464, 1380)
(-24, 6344)
(459, -8560)
(-216, 7640)
(552, 11032)
(-434, 4130)

Commentary

BASE records/rank_9.md#13 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:23:31 UTC · history

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