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curve #1590

y² + xy + y = x³ − 1402210x + 638980920

a-invariants: [1, 0, 1, -1402210, 638980920]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/3ℤ
conductor (N): 11281858 ☆ record for ℤ/3ℤ torsion, rank ≥ 4
discriminant (Δ): 144715980196844
Faltings height: 2.0540
naive height: 54.0743
primes of bad reduction: 2, 7, 19, 73, 83
regulator: 17.52098565132778778548726755250636687102104120
submitted by: Michael Rubinstein
submitted at: 2026-09-25 01:23:30 UTC
last updated: 2026-09-25 01:23:30 UTC

Witness: 4 independent points log in to add more points →

(55309/81, -271333/729)
(109, -22133)
(684, -352)
(6973/16, -687357/64)

Commentary

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

last edited by Michael Rubinstein at 2026-09-25 01:23:30 UTC · history

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