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curve #3446

y² = x³ + x² − 49344519305x + 3002551554488119

a-invariants: [0, 1, 0, -49344519305, 3002551554488119]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 45709648312790275648
discriminant (Δ): 3794816817859786150114547346870272
Faltings height: 5.1498
naive height: 85.4799
primes of bad reduction: 2, 17, 89, 223, 257, 271, 433, 4129
regulator: 443655.45997781333593370432074343419245096919212615070279
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:35:00 UTC
last updated: 2026-09-27 05:35:00 UTC

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

(49447, 26144096)
(181545, 5272612)
(195817, -29130044)
(51759, -24232072)
(-61971, 76305248)
(-90361, 81997392)
(252682, -81654349)
(-47699, -72441104)
(181299, -3955832)

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 05:35:00 UTC · history

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