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curve #3450

y² = x³ − x² − 16280580185x + 796131389503641

a-invariants: [0, -1, 0, -16280580185, 796131389503641]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 55660539421203992256
discriminant (Δ): 2369585980829085281059075264512
Faltings height: 4.6758
naive height: 82.1533
primes of bad reduction: 2, 3, 41, 73, 97, 113, 127, 353, 439, 449
regulator: 278159.03332593483623556292694600291242969448058912411234
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:35:42 UTC
last updated: 2026-09-27 05:35:42 UTC

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

(162743, -49566612)
(45761, -12121896)
(67877, -1943880)
(842185/9, 259041608/27)
(95576, 10637409)
(-92755, 38835696)
(12005, -24544104)
(41579, 13823232)
(81089, 3023832)

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 05:35:42 UTC · history

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