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curve #1472

y² = x³ + x² − 19315920x + 54017604468

a-invariants: [0, 1, 0, -19315920, 54017604468]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/8ℤ
conductor (N): 895440
discriminant (Δ): -799594825835479103539200
Faltings height: 3.2822
naive height: 62.9485
primes of bad reduction: 2, 3, 5, 7, 13, 41
regulator: 9.27261750438582768965152417019587596014551
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:16:18 UTC
last updated: 2026-09-25 00:16:18 UTC

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

(-3138, 289380)
(-2709, 294060)

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 00:16:19 UTC · history

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