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curve #1478

y² + xy + y = x³ − x² − 44384149544567x + 113812511738016628559

a-invariants: [1, -1, 1, -44384149544567, 113812511738016628559]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/9ℤ
conductor (N): 409799790
discriminant (Δ): 51727376376891321596610048000000000
Faltings height: 6.2767
naive height: 105.8853
primes of bad reduction: 2, 3, 5, 17, 19, 37, 127
regulator: 38.9196469851584430859088729479588677760990
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:22:19 UTC
last updated: 2026-09-25 00:22:19 UTC

Witness: 2 independent points log in to add more points →

(44635753/9, 106837934782/27)
(376850069523/97969, -48663447272498/30664297)

Commentary

Torsion Z/9. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:22:19 UTC · history

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