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curve #1690

y² + xy + y = x³ + x² − 405923809938x + 81592736994785406

a-invariants: [1, 1, 1, -405923809938, 81592736994785406]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/4ℤ
conductor (N): 33309463270425
discriminant (Δ): 1404689967527888345795098904382890625
Faltings height: 5.6536
naive height: 91.8019
primes of bad reduction: 3, 5, 31, 41, 59, 61, 79, 1229
regulator: 2041.3272286000935485272246762640743493279308847987
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:10:38 UTC
last updated: 2026-09-25 06:10:38 UTC

Witness: 6 independent points log in to add more points →

(678015, -343933708)
(4458856/9, 1227488926/27)
(140815, 164928992)
(578890, -201788458)
(182293315/196, -1958174000777/2744)
(490390, -21744058)

Commentary

Torsion Z/4. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:10:38 UTC · history

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