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curve #1511

y² + xy + y = x³ − x² − 6367505x + 308556093872

a-invariants: [1, -1, 1, -6367505, 308556093872]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 15162762825
discriminant (Δ): -41112417505475228795859375
Faltings height: 3.5939
naive height: 66.4335
primes of bad reduction: 3, 5, 7, 17, 47, 12049
regulator: 160.6646571800632880461481488128896437781465840
submitted by: hdeping
submitted at: 2026-09-25 00:43:48 UTC
last updated: 2026-09-25 00:43:48 UTC

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

(-8309/4, 4482705/8)
(1389, 549205)
(-186, 556630)
(189, 554305)

Commentary

Specialization t=799/735 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 08:27:34 UTC · history

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