curve #2971

y² + xy = x³ − 147899x + 21811944

a-invariants: [1, 0, 0, -147899, 21811944]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 102297
discriminant (Δ): 1289258573625009
Faltings height: 1.7606
naive height: 47.3265
primes of bad reduction: 3, 13, 43, 61
regulator: 7.89215400433262179791218735151313604685613
submitted by: David Renshaw
submitted at: 2026-09-26 20:31:05 UTC
last updated: 2026-09-26 20:31:05 UTC

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

(244, 394)
(-57, 5511)

Commentary

Cremona 102297f2 = LMFDB 102297.d4: https://www.lmfdb.org/EllipticCurve/Q/102297/d/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 102297, minimal discriminant 1289258573625009, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:31:05 UTC · history