curve #3130

y² = x³ − x² − 196x + 196

a-invariants: [0, -1, 0, -196, 196]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 10920
discriminant (Δ): 476985600
Faltings height: 0.3551
naive height: 27.4530
primes of bad reduction: 2, 3, 5, 7, 13
regulator: 0.877193932573383289231614190388608448021710
submitted by: David Renshaw
submitted at: 2026-09-26 20:38:41 UTC
last updated: 2026-09-26 20:38:41 UTC

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

(0, 14)
(-4, 30)

Commentary

Cremona 10920k2 = LMFDB 10920.a3: https://www.lmfdb.org/EllipticCurve/Q/10920/a/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 10920, minimal discriminant 476985600, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:38:42 UTC · history