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curve #1409

y² + xy = x³ − 118420034924296586x + 15685104898890172023674916

a-invariants: [1, 0, 0, -118420034924296586, 15685104898890172023674916]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/12ℤ
conductor (N): 5960311890
discriminant (Δ): -752258682280058735862282494648154092281528320000
Faltings height: 8.3967
naive height: 129.5527
primes of bad reduction: 2, 3, 5, 13, 157, 311, 313
regulator: 145.940315181359336411857676789208387287808
submitted by: Michael Rubinstein
submitted at: 2026-09-24 23:24:17 UTC
last updated: 2026-09-24 23:24:17 UTC

Witness: 2 independent points log in to add more points →

(1014772465816564/5121169, 170975092752356183434/11589205447)
(1249863053030644/6285049, 135500105511564482546/15756617843)

Commentary

Torsion Z/12. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-24 23:24:17 UTC · history

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