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curve #4050

y² = x³ + x² − 3664351889x + 70791863393391

a-invariants: [0, 1, 0, -3664351889, 70791863393391]
c-invariants: [175888890688, -61165225305233920]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 6123114630336
discriminant (Δ): 983954030179505302081574682624
Faltings height: 4.4740
naive height: 77.6794
primes of bad reduction: 2, 3, 11, 23, 47, 59, 131, 347
regulator: 833.65556125944227203428873554506967517764438064415
submitted by: Michael Rubinstein
submitted at: 2026-10-07 22:24:34 UTC
last updated: 2026-10-07 22:24:34 UTC

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

(6415, 6895584)
(54301, 5650548)
(1063855/49, 415683792/343)
(1309639/25, 594169488/125)
(87613, 20549340)
(1603201/25, 1247051376/125)

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 2026-10-07 22:24:34 UTC · history

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