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curve #3455

y² = x³ + x² − 7054975769x + 224370503788711

a-invariants: [0, 1, 0, -7054975769, 224370503788711]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 59674364161385812544
discriminant (Δ): 725031681347828697135699267584
Faltings height: 4.5238
naive height: 79.6446
primes of bad reduction: 2, 17, 89, 271, 409, 463, 7937
regulator: 490528.55791061248932786212342989478627916883842226542859
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:37:52 UTC
last updated: 2026-09-27 05:37:52 UTC

Witness: 9 independent points log in to add more points →

(5221, 13699592)
(35031, 4496432)
(84943, 15427160)
(-196187/4, 170159545/8)
(-1009, 15214728)
(53730, 650671)
(3333643, 6084741320)
(67009, 7246540)
(6901530/169, 4592437273/2197)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-27 05:37:52 UTC · history

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