curve #2773

y² + xy = x³ + x² − 23x + 33

a-invariants: [1, 1, 0, -23, 33]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 210
discriminant (Δ): 44100
Faltings height: -0.3330
naive height: 21.0873
primes of bad reduction: 2, 3, 5, 7
regulator: 0.2663232904778722809637337277061304606040
submitted by: David Renshaw
submitted at: 2026-09-26 20:21:47 UTC
last updated: 2026-09-26 20:21:47 UTC

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

(4, 3)

Commentary

Cremona 210d2 = LMFDB 210.a2: https://www.lmfdb.org/EllipticCurve/Q/210/a/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 210, minimal discriminant 44100, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:21:47 UTC · history