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curve #1497

y² = x³ + x² + 415x + 3199

a-invariants: [0, 1, 0, 415, 3199]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
conductor (N): 61376
discriminant (Δ): -8610316288
Faltings height: 0.5929
naive height: 29.6960
primes of bad reduction: 2, 7, 137
regulator: 4.4662107762872055811400695032377684366807333
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:41:19 UTC
last updated: 2026-09-25 00:41:19 UTC

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

(-5, 32)
(11, 96)
(43, 320)

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 00:41:19 UTC · history

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