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curve #1694

y² + xy = x³ − 6769521299x + 122205015087249

a-invariants: [1, 0, 0, -6769521299, 122205015087249]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 39992228166
discriminant (Δ): 13402690729741432927557140768784
Faltings height: 4.6715
naive height: 79.5207
primes of bad reduction: 2, 3, 11, 19, 73, 347, 1259
regulator: 537.5666364914499495940147918932768862458427682
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:11:18 UTC
last updated: 2026-09-25 06:11:18 UTC

Witness: 4 independent points log in to add more points →

(18064, 2402377)
(96028, 18863731)
(-373451/16, 1047483901/64)
(2900806/9, 4781862839/27)

Commentary

Torsion Z/4+Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:11:18 UTC · history

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