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curve #1648

y² + xy + y = x³ + x² − 526541188x + 4274187959156

a-invariants: [1, 1, 1, -526541188, 4274187959156]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/4ℤ
conductor (N): 267725942025
discriminant (Δ): 1449918186048699063342890625
Faltings height: 3.9515
naive height: 71.8591
primes of bad reduction: 3, 5, 17, 41, 79, 241, 269
regulator: 787.361799948194162486451322196085973916377135082
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:23:19 UTC
last updated: 2026-09-25 02:23:19 UTC

Witness: 5 independent points log in to add more points →

(33655/4, -5338509/8)
(-109946/9, 80639480/27)
(661256/25, 370269831/125)
(18839, -1029828)
(-59165/4, -23708539/8)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:23:19 UTC · history

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