curve #2993

y² + xy = x³ + 250x − 1725

a-invariants: [1, 0, 0, 250, -1725]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/4ℤ
conductor (N): 22515
discriminant (Δ): -2316455775
Faltings height: 0.4827
naive height: 28.4531
primes of bad reduction: 3, 5, 19, 79
regulator: 7.22815580881490801666629265464477590214817
submitted by: David Renshaw
submitted at: 2026-09-26 20:32:22 UTC
last updated: 2026-09-26 20:32:22 UTC

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

(7, 16)
(70, 565)

Commentary

Cremona 22515f1 = LMFDB 22515.e4: https://www.lmfdb.org/EllipticCurve/Q/22515/e/4 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 22515, minimal discriminant -2316455775, torsion ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:32:22 UTC · history