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curve #1542

y² + xy = x³ − x² − 3427857792x + 77244619601268

a-invariants: [1, -1, 0, -3427857792, 77244619601268]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/6ℤ
conductor (N): 3091842
discriminant (Δ): 224210046590204496952000572
Faltings height: 4.1268
naive height: 77.4792
primes of bad reduction: 2, 3, 13, 73, 181
regulator: 31.142208045854742770236733443884557891440740
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:52:41 UTC
last updated: 2026-09-25 00:52:41 UTC

Witness: 3 independent points log in to add more points →

(33507, 57366)
(28737048/841, 2066061930/24389)
(97454766, 962016558942)

Commentary

Torsion Z/6. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:52:41 UTC · history

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