curve #2925

y² + xy + y = x³ − 74x + 72

a-invariants: [1, 0, 1, -74, 72]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
conductor (N): 325430
discriminant (Δ): 22780100
Faltings height: 0.1038
naive height: 24.5063
primes of bad reduction: 2, 5, 7, 4649
regulator: 2.8610559810006646002878997685082151371473513
submitted by: David Renshaw
submitted at: 2026-09-26 20:28:39 UTC
last updated: 2026-09-26 20:28:39 UTC

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

(-9, 9)
(-6, 20)
(15, 41)

Commentary

Cremona 325430a1 = LMFDB 325430.a1: https://www.lmfdb.org/EllipticCurve/Q/325430/a/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 325430, minimal discriminant 22780100, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:28:39 UTC · history