curve #2882

y² = x³ − x² − 174x + 504

a-invariants: [0, -1, 0, -174, 504]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 21216
discriminant (Δ): 253191744
Faltings height: 0.3087
naive height: 27.0965
primes of bad reduction: 2, 3, 13, 17
regulator: 3.75248831544398869761568820361457024176983
submitted by: David Renshaw
submitted at: 2026-09-26 20:26:41 UTC
last updated: 2026-09-26 20:26:41 UTC

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

(-6, 36)
(-13, 20)

Commentary

Cremona 21216l1 = LMFDB 21216.d3: https://www.lmfdb.org/EllipticCurve/Q/21216/d/3 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 21216, minimal discriminant 253191744, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:26:41 UTC · history