curve #3295

y² + xy = x³ − 1129x + 14480

a-invariants: [1, 0, 0, -1129, 14480]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 12207
discriminant (Δ): 347057217
Faltings height: 0.5222
naive height: 32.7009
primes of bad reduction: 3, 13, 313
regulator: 2.40548049928273706958080543195754910568476
submitted by: David Renshaw
submitted at: 2026-09-26 20:53:13 UTC
last updated: 2026-09-26 20:53:13 UTC

Witness: 2 independent points log in to add more points →

(17, 8)
(23, 17)

Commentary

Cremona 12207e1 = LMFDB 12207.b3: https://www.lmfdb.org/EllipticCurve/Q/12207/b/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 12207, minimal discriminant 347057217, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:53:13 UTC · history