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curve #1513

y² + xy = x³ − x² − 324x − 896

a-invariants: [1, -1, 0, -324, -896]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
conductor (N): 69966
discriminant (Δ): 1768180752
Faltings height: 0.4687
naive height: 28.9576
primes of bad reduction: 2, 3, 13, 23
regulator: 1.6361524294842749807549366092118626115085150
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:44:18 UTC
last updated: 2026-09-25 00:44:18 UTC

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

(-4, -16)
(20, -28)
(32, 128)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:44:19 UTC · history

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