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curve #3459

y² + xy + y = x³ − 13693841992220x + 19491670055901696510

a-invariants: [1, 0, 1, -13693841992220, 19491670055901696510]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/3ℤ
conductor (N): 72865681816774464982
discriminant (Δ): 217072513013507699543036794738086818444
Faltings height: 6.2883
naive height: 102.3575
primes of bad reduction: 2, 7, 13, 83, 349, 463, 661, 2137, 3019
regulator: 249175.778408709601909537243660545239186280848175959299
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:39:06 UTC
last updated: 2026-09-27 05:39:06 UTC

Witness: 8 independent points log in to add more points →

(-3924703, -3573311611)
(-1016137, 5688855229)
(19862385, 87073333985)
(10716283, 33211939307)
(2082259, -77259727)
(-4117311, 2466971573)
(976207587/484, -2965313601639/10648)
(-537075360/169, 12219000475170/2197)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-27 05:39:06 UTC · history

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