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curve #1667

y² + xy = x³ − x² − 2726502298494x + 420710024996378208

a-invariants: [1, -1, 0, -2726502298494, 420710024996378208]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/6ℤ
conductor (N): 40432009593690
discriminant (Δ): 1220709614145627203684831823251568466500
Faltings height: 6.1909
naive height: 97.5157
primes of bad reduction: 2, 3, 5, 11, 13, 31, 47, 463, 4657
regulator: 3381.97869324530651025300790657211832882616984739
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:48:19 UTC
last updated: 2026-09-25 02:48:19 UTC

Witness: 5 independent points log in to add more points →

(51493/9, 17184965278/27)
(1601032, 398475764)
(3389843799/625, 188226641748732/15625)
(-637437, 1378606056)
(50892106/25, 227163389956/125)

Commentary

Torsion Z/6. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:48:19 UTC · history

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