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curve #1510

y² + xy + y = x³ − x² − 2722451x + 4697700882

a-invariants: [1, -1, 1, -2722451, 4697700882]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 2042704917
discriminant (Δ): -8239385953009075585743
Faltings height: 2.8910
naive height: 58.0635
primes of bad reduction: 3, 11, 31, 37, 17989
regulator: 156.5276683242142980618951557109489556792343123
submitted by: hdeping
submitted at: 2026-09-25 00:43:40 UTC
last updated: 2026-09-25 00:43:40 UTC

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

(-7665/4, 436639/8)
(92069/16, 26934351/64)
(-2092, 36177)
(284765/16, 150796587/64)

Commentary

Specialization t=1147/363 of the Kubert-Tate torsion Z/4 universal family y^2+xy+ty=x^3+tx^2.

last edited by hdeping at 2026-09-27 08:27:17 UTC · history

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