curve #2817

y² = x³ + x² − 11517x + 471871

a-invariants: [0, 1, 0, -11517, 471871]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/3ℤ
conductor (N): 447764
discriminant (Δ): 15159497984
Faltings height: 0.9934
naive height: 39.6684
primes of bad reduction: 2, 23, 31, 157
regulator: 12.054093319166366349113431520062521951543033
submitted by: David Renshaw
submitted at: 2026-09-26 20:23:45 UTC
last updated: 2026-09-26 20:23:45 UTC

Witness: 3 independent points log in to add more points →

(61, 6)
(57, 62)
(-79, 946)

Commentary

Cremona 447764a1 = LMFDB 447764.a2: https://www.lmfdb.org/EllipticCurve/Q/447764/a/2 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 447764, minimal discriminant 15159497984, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:23:45 UTC · history