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curve #2127

y² + y = x³ + x² + 343x + 29412

a-invariants: [0, 1, 1, 343, 29412]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/3ℤ
conductor (N): 64771
discriminant (Δ): -373391925571
Faltings height: 0.9000
naive height: 34.0937
primes of bad reduction: 7, 19, 487
regulator: 6.50200863528541439433567954275579905392325
submitted by: hdeping
submitted at: 2026-09-26 10:37:44 UTC
last updated: 2026-09-26 10:37:44 UTC

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

(28, 248)
(245/4, 4259/8)

Commentary

Specialization of the torsion Z/3 family E: y^2+a*x*y+b^3*y=x^3, arising from x/y+y/z+z/x = k with k = 30+2/7.

last edited by hdeping at 2026-09-27 08:33:57 UTC · history

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