curve #1047

y² + xy + y = x³ − 286854x + 58872856

a-invariants: [1, 0, 1, -286854, 58872856]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 2310 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 1
discriminant (Δ): 12104550027662400
Faltings height: 1.9364
naive height: 49.3138
primes of bad reduction: 2, 3, 5, 7, 11
regulator: 1.663762100901515510587480200826255368251
submitted by: David Renshaw
submitted at: 2026-09-23 15:20:47 UTC
last updated: 2026-09-23 15:20:47 UTC

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

(269, 957)

Commentary

Cremona 2310g2 = LMFDB 2310.h5: https://www.lmfdb.org/EllipticCurve/Q/2310/h/5 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 2310, minimal discriminant 12104550027662400, torsion ℤ/2ℤ × ℤ/6ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:20:47 UTC · history