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curve #1526

y² + xy + y = x³ − x² − 554036x + 158865630

a-invariants: [1, -1, 1, -554036, 158865630]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/4ℤ
conductor (N): 503217
discriminant (Δ): 179630273176497
Faltings height: 1.8971
naive height: 51.2886
primes of bad reduction: 3, 11, 13, 17, 23
regulator: 6.4726489398058194026655425055059642720940616
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:50:00 UTC
last updated: 2026-09-25 00:50:00 UTC

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

(-402, 17991)
(-844, 5394)
(794, 14403)

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 00:50:00 UTC · history

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