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curve #1512

y² = x³ − 230691x + 2665786466

a-invariants: [0, 0, 0, -230691, 2665786466]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/4ℤ
conductor (N): 90471312
discriminant (Δ): -3069186624901911195648
Faltings height: 2.8019
naive height: 56.9307
primes of bad reduction: 2, 3, 19, 43, 769
regulator: 61.42929209968493216920811791866876745367539085
submitted by: hdeping
submitted at: 2026-09-25 00:43:55 UTC
last updated: 2026-09-25 00:43:55 UTC

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

(5911, 455886)
(-1271, 30096)
(-1385, 18126)
(-1399, 15824)

Commentary

Specialization t=817/768 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 08:26:47 UTC · history

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