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curve #4483

y² + y = x³ − 243817x + 39472236

a-invariants: [0, 0, 1, -243817, 39472236]
c-invariants: [11703216, -34104012120]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 254543075867697157
discriminant (Δ): 254543075867697157
Faltings height: 2.0625
naive height: 48.8261
primes of bad reduction: 786613, 323593782289
regulator: 2282667.2304590168633224567562299701720564168169332051942
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:30:58 UTC
last updated: 2026-10-17 10:30:58 UTC

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

(-560, 627)
(-557, 1571)
(-542, 3521)
(-517, 5228)
(-513, 5435)
(-498, 6114)
(-472, 7028)
(-219, 9075)
(25913, 4170596)

Commentary

BASE records/rank_9.md#16 + Werr 4-Pillar Multi-Layer Algebraic Sieve conductor factorization.

last edited by Volkan Dagli at 2026-10-17 10:30:58 UTC · history

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