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curve #1412

y² + xy + y = x³ + x² + 6x + 42

a-invariants: [1, 1, 1, 6, 42]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ
conductor (N): 1443
discriminant (Δ): -694083
Faltings height: -0.1991
naive height: 20.8852
primes of bad reduction: 3, 13, 37
regulator: 0.790463101484975738716171228728583121090222
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:24:47 UTC
last updated: 2026-09-24 23:24:47 UTC

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

(0, 6)
(3, 8)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 23:24:47 UTC · history

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