curve #2966

y² + xy + y = x³ + x² − 48195x + 3122520

a-invariants: [1, 1, 1, -48195, 3122520]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 262605
discriminant (Δ): 2898102247700625
Faltings height: 1.6787
naive height: 43.9626
primes of bad reduction: 3, 5, 7, 41, 61
regulator: 9.30821061243579413428147233035497958507094
submitted by: David Renshaw
submitted at: 2026-09-26 20:30:46 UTC
last updated: 2026-09-26 20:30:46 UTC

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

(9, 1635)
(-116, 2735)

Commentary

Cremona 262605c2 = LMFDB 262605.c3: https://www.lmfdb.org/EllipticCurve/Q/262605/c/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 262605, minimal discriminant 2898102247700625, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:30:46 UTC · history