curve #2867

y² + xy = x³ − 15x

a-invariants: [1, 0, 0, -15, 0]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 465
discriminant (Δ): 216225
Faltings height: -0.2868
naive height: 19.7419
primes of bad reduction: 3, 5, 31
regulator: 1.093567343958523129336386005379178616190
submitted by: David Renshaw
submitted at: 2026-09-26 20:26:03 UTC
last updated: 2026-09-26 20:26:03 UTC

Witness: 1 independent point log in to add more points →

(5, 5)

Commentary

Cremona 465b2 = LMFDB 465.a2: https://www.lmfdb.org/EllipticCurve/Q/465/a/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 465, minimal discriminant 216225, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:26:03 UTC · history