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curve #3458

y² + xy + y = x³ − 82065445090x + 9018653912336840

a-invariants: [1, 0, 1, -82065445090, 9018653912336840]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 18526405288385514
discriminant (Δ): 234853151215298991425360541823644
Faltings height: 5.0698
naive height: 87.0060
primes of bad reduction: 2, 3, 13, 19, 23, 29, 31, 271, 96997
regulator: 3656.035387977615697156776853885135265011070623256691
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:38:23 UTC
last updated: 2026-09-27 05:38:23 UTC

Witness: 7 independent points log in to add more points →

(146647, 11661323)
(311947, 117208679)
(116608, 32109047)
(31048, -80641921)
(111934, 35089292)
(2669125, 4335188615)
(154912, 4746824)

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 05:38:23 UTC · history

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