curve #1053

y² + xy = x³ − 544326x + 154522980

a-invariants: [1, 0, 0, -544326, 154522980]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 3570
discriminant (Δ): 770635366502400
Faltings height: 1.9353
naive height: 51.2355
primes of bad reduction: 2, 3, 5, 7, 17
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:21:51 UTC
last updated: 2026-09-23 15:21:51 UTC

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Commentary

Cremona 3570v2 = LMFDB 3570.w6: https://www.lmfdb.org/EllipticCurve/Q/3570/w/6 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 3570, minimal discriminant 770635366502400, torsion ℤ/2ℤ × ℤ/6ℤ.

last edited by David Renshaw at 2026-09-23 15:21:51 UTC · history