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curve #3449

y² + y = x³ + x² − 37352633327x + 2777874222289905

a-invariants: [0, 1, 1, -37352633327, 2777874222289905]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/3ℤ
conductor (N): 15554489496586229
discriminant (Δ): 1772468106318135923654883491909
Faltings height: 4.7809
naive height: 84.6446
primes of bad reduction: 7, 19, 73, 197, 223, 673, 7741
regulator: 130965.5267585873765608954604737873229596815925344659
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:35:32 UTC
last updated: 2026-09-27 05:35:32 UTC

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

(58873, 27979844)
(79431, 17665679)
(113315, 520375)
(89393825/841, -71005228780/24389)
(146589301/961, 747416374925/29791)
(-26504427/841, 1527724233871/24389)
(-1372591/16, 4681594207/64)

Commentary

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

last edited by Michael Rubinstein at 2026-09-27 05:35:32 UTC · history

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