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curve #4350

y² + xy = x³ − 1034398205x + 9475169986800

a-invariants: [1, 0, 0, -1034398205, 9475169986800]
c-invariants: [49651113841, -8186621345265961]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 19891394744835
discriminant (Δ): 32049074376482805835493355225
Faltings height: 4.1786
naive height: 73.8849
primes of bad reduction: 3, 5, 29, 181, 349, 709, 1021
regulator: 3935.9187482292263367326897986589068192424799813738
submitted by: Volkan Dagli
submitted at: 2026-10-17 10:05:51 UTC
last updated: 2026-10-17 10:05:51 UTC

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

(108595/4, 9366755/8)
(-4523, 3752092)
(10135, 175540)
(70624/9, -36743956/27)
(25927, -304283)
(7465, 1469155)

Commentary

BASE torsion/torsion_Z2xZ2.tsv.gz:58 (mrubinst/elliptic-curves-by-rank) + conductor prime factorization via pCwOrM Werr 4-Pillar Algebraic Sieve.

last edited by Volkan Dagli at 2026-10-17 10:05:51 UTC · history

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