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curve #1305

y² = x³ − 6444371892x + 156806810185376

a-invariants: [0, 0, 0, -6444371892, 156806810185376]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 11336746656960
discriminant (Δ): 6506417378682245380769856000000
Faltings height: 4.6261
naive height: 79.3730
primes of bad reduction: 2, 3, 5, 47, 53, 79, 83, 241
regulator: 835.79006987221758450351150671197449375121939380988
submitted by: Michael Rubinstein
submitted at: 2026-09-24 17:29:04 UTC
last updated: 2026-09-24 17:29:04 UTC

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

(15142, 7918200)
(-15068, 15826860)
(67930, 5701104)
(63142, 1279800)
(576178/9, 69504200/27)
(-9758, 14790600)

Commentary

Torsion Z/2+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 17:29:04 UTC · history

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