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curve #1471

y² + xy + y = x³ + x² − 72485224x + 236624449385

a-invariants: [1, 1, 1, -72485224, 236624449385]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/8ℤ
conductor (N): 659022
discriminant (Δ): 179747907033605127340032
Faltings height: 3.3160
naive height: 65.9103
primes of bad reduction: 2, 3, 7, 13, 17, 71
regulator: 11.6407403859762630711447686822206296024438
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:15:19 UTC
last updated: 2026-09-25 00:15:19 UTC

Witness: 2 independent points log in to add more points →

(1166645/49, 1184511147/343)
(111349/25, -6087303/125)

Commentary

Torsion Z/8. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:15:19 UTC · history

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