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curve #1539

y² + xy + y = x³ − x² − 2421065x + 1514996489

a-invariants: [1, -1, 1, -2421065, 1514996489]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/6ℤ
conductor (N): 2327418 ☆ record for ℤ/6ℤ torsion, rank ≥ 3
discriminant (Δ): -82503571421707806528
Faltings height: 2.5810
naive height: 55.7997
primes of bad reduction: 2, 3, 31, 43, 97
regulator: 58.557838857099563341220508202155192847728522
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:52:11 UTC
last updated: 2026-09-25 00:52:11 UTC

Witness: 3 independent points log in to add more points →

(-1199, 52494)
(-1773, 16108)
(2097, 74158)

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 00:52:11 UTC · history

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