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curve #4101

y² = x³ + x² − 31270732033x + 1543781323364063

a-invariants: [0, 1, 0, -31270732033, 1543781323364063]
c-invariants: [1500995137600, -1333836069357376000]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 6767505067200
discriminant (Δ): 927432277900197949445760000000000
Faltings height: 5.0335
naive height: 84.1114
primes of bad reduction: 2, 3, 5, 41, 173, 197, 1009
regulator: 2929.7515631458810604526083179811773886286815676712
submitted by: Michael Rubinstein
submitted at: 2026-10-09 14:51:44 UTC
last updated: 2026-10-09 14:51:44 UTC

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

(18563, 31140000)
(-176062, 39898125)
(-197341, 5447424)
(-4477, 41032800)
(-37687, 51660000)
(148313, -12975000)

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 2026-10-09 14:51:44 UTC · history

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