curve #3247

y² + y = x³ − 534x + 4752

a-invariants: [0, 0, 1, -534, 4752]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/3ℤ
conductor (N): 153
discriminant (Δ): -10744731
Faltings height: 0.2901
naive height: 30.4559
primes of bad reduction: 3, 17
regulator: 0.3386692155049187147489901770147896127612
submitted by: David Renshaw
submitted at: 2026-09-26 20:45:25 UTC
last updated: 2026-09-26 20:45:25 UTC

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

(14, 4)

Commentary

Cremona 153b2 = LMFDB 153.b1: https://www.lmfdb.org/EllipticCurve/Q/153/b/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 153, minimal discriminant -10744731, torsion ℤ/3ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:45:25 UTC · history