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curve #1515

y² = x³ − x² − 825x + 9801

a-invariants: [0, -1, 0, -825, 9801]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
conductor (N): 80256
discriminant (Δ): -3220512768
Faltings height: 0.5843
naive height: 31.8467
primes of bad reduction: 2, 3, 11, 19
regulator: 0.83188845131482684596405302548819427384967183
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:46:19 UTC
last updated: 2026-09-25 00:46:19 UTC

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

(33, -132)
(11, 44)
(-11, 132)

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 00:46:19 UTC · history

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