curve #2914

y² + xy + y = x³ − 12x − 10

a-invariants: [1, 0, 1, -12, -10]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ
conductor (N): 4606
discriminant (Δ): 64484
Faltings height: -0.3779
naive height: 18.9461
primes of bad reduction: 2, 7, 47
regulator: 0.929565467008945818817579607248032689368737
submitted by: David Renshaw
submitted at: 2026-09-26 20:28:10 UTC
last updated: 2026-09-26 20:28:10 UTC

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

(4, 1)
(-2, 3)

Commentary

Cremona 4606d1 = LMFDB 4606.a2: https://www.lmfdb.org/EllipticCurve/Q/4606/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 4606, minimal discriminant 64484, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:28:10 UTC · history