curve #2712

y² + xy = x³ − 106x + 420

a-invariants: [1, 0, 0, -106, 420]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/6ℤ
conductor (N): 310
discriminant (Δ): -3174400
Faltings height: 0.0333
naive height: 25.6453
primes of bad reduction: 2, 5, 31
regulator: 0.9776191070965400572788433675257063742869
submitted by: David Renshaw
submitted at: 2026-09-26 20:18:52 UTC
last updated: 2026-09-26 20:18:52 UTC

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

(6, 0)

Commentary

Cremona 310b1 = LMFDB 310.a3: https://www.lmfdb.org/EllipticCurve/Q/310/a/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 310, minimal discriminant -3174400, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:18:52 UTC · history