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curve #1505

y² = x³ + 174270951x + 30369364569

a-invariants: [0, 0, 0, 174270951, 30369364569]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/3ℤ
conductor (N): 898024821876
discriminant (Δ): -339129458765688772265391216
Faltings height: 3.7802
naive height: 68.5420
primes of bad reduction: 2, 3, 7, 13, 41, 18119
regulator: 175.7940567356378087355118779988051554937633309
submitted by: hdeping
submitted at: 2026-09-25 00:43:12 UTC
last updated: 2026-09-25 00:43:12 UTC

Witness: 4 independent points log in to add more points →

(1221, 494949)
(1312, 511147)
(2337/16, 15121743/64)
(2091, 635541)

Commentary

Specialization t=246/91 of the universal torsion Z/3 family y^2+txy+ty=x^3 (Tate normal form).

last edited by hdeping at 2026-09-27 08:27:50 UTC · history

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