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curve #3438

y² + xy = x³ − x² − 324141x + 89192321

a-invariants: [1, -1, 0, -324141, 89192321]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
conductor (N): 3123097398
discriminant (Δ): -1250805511101031596
Faltings height: 2.1847 ☆ record for ℤ/3ℤ torsion, rank ≥ 5
naive height: 50.1339 ☆ record for ℤ/3ℤ torsion, rank ≥ 5
primes of bad reduction: 2, 3, 53, 61, 67, 89
regulator: 136.106723351762480281431683163649792271274581148
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:33:39 UTC
last updated: 2026-09-27 05:33:39 UTC

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

(4844, 332485)
(-674, 1405)
(-668, 3037)
(14659/4, 1740065/8)
(-10976/25, 1541597/125)

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 05:33:39 UTC · history

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