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curve #1333

y² = x³ − x² − 159733785x + 776778430041

a-invariants: [0, -1, 0, -159733785, 776778430041]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ
conductor (N): 54381804383424
discriminant (Δ): 211207675977310232973312
Faltings height: 3.4315
naive height: 68.2807
primes of bad reduction: 2, 3, 7, 31, 97, 113, 193, 617
regulator: 1843.503494542389652047750500001027242516695994830532
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:33:50 UTC
last updated: 2026-09-24 17:33:50 UTC

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

(1163, 769792)
(7425, 6696)
(49275, 10608696)
(3333, 530472)
(6960, 46221)
(4461, 391104)
(14121, 1156176)

Commentary

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

last edited by Michael Rubinstein at 2026-09-24 17:33:50 UTC · history

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