curve #3281

y² = x³ − 156x + 736

a-invariants: [0, 0, 0, -156, 736]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 288
discriminant (Δ): 8957952
Faltings height: 0.1231
naive height: 26.7632
primes of bad reduction: 2, 3
regulator: 0.6201696728496703763000034731367110194813
submitted by: David Renshaw
submitted at: 2026-09-26 20:50:56 UTC
last updated: 2026-09-26 20:50:56 UTC

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

(5, 9)

Commentary

Cremona 288b3 = LMFDB 288.b2: https://www.lmfdb.org/EllipticCurve/Q/288/b/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 288, minimal discriminant 8957952, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:50:57 UTC · history