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curve #1236

y² + xy = x³ + x² − 82433x + 8186337

a-invariants: [1, 1, 0, -82433, 8186337]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 146635526910
discriminant (Δ): 6655786566444900
Faltings height: 1.7703 ☆ record for ℤ/2ℤ torsion, rank ≥ 6
naive height: 45.5728 ☆ record for ℤ/2ℤ torsion, rank ≥ 6
primes of bad reduction: 2, 3, 5, 17, 89, 769, 4201
regulator: 270.84233445781857523226231608984325494739678277050
submitted by: Michael Rubinstein
submitted at: 2026-09-24 14:37:21 UTC
last updated: 2026-09-24 14:37:21 UTC

Witness: 6 independent points log in to add more points →

(-328, 431)
(-304, 2447)
(-239, 3902)
(376, 5337)
(-202, 4181)
(-689/4, 33975/8)

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 14:37:21 UTC · history

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