curve #3298

y² = x³ − x² − 42959x + 3441480

a-invariants: [0, -1, 0, -42959, 3441480]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 54264
discriminant (Δ): 2062032
Faltings height: 1.0309
naive height: 43.6176
primes of bad reduction: 2, 3, 7, 17, 19
regulator: 18.0930736841915696104581497478936106729208
submitted by: David Renshaw
submitted at: 2026-09-26 20:53:42 UTC
last updated: 2026-09-26 20:53:42 UTC

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

(520, 11020)
(241, 2651)

Commentary

Cremona 54264h1 = LMFDB 54264.b4: https://www.lmfdb.org/EllipticCurve/Q/54264/b/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 54264, minimal discriminant 2062032, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:53:42 UTC · history