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curve #3463

y² + xy = x³ − 199700187x + 1086437663569

a-invariants: [1, 0, 0, -199700187, 1086437663569]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/3ℤ
conductor (N): 29709620122
discriminant (Δ): -224551308746039238885376
Faltings height: 3.4669
naive height: 68.9510
primes of bad reduction: 2, 7, 13, 23, 37, 67, 409
regulator: 71.9334841794358268219948132460421944208328492066
submitted by: Michael Rubinstein
submitted at: 2026-09-27 05:42:17 UTC
last updated: 2026-09-27 05:42:17 UTC

Witness: 5 independent points log in to add more points →

(8838, 104417)
(10658, 405445)
(4974, 462481)
(2398, 787057)
(-738, 1110961)

Commentary

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-27 05:42:17 UTC · history

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