curve #3285

y² = x³ − x² − 175x + 952

a-invariants: [0, -1, 0, -175, 952]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 840
discriminant (Δ): 8400
Faltings height: -0.1068
naive height: 27.1137
primes of bad reduction: 2, 3, 5, 7
regulator: 2.196597963753069286457897954426581558085
submitted by: David Renshaw
submitted at: 2026-09-26 20:51:35 UTC
last updated: 2026-09-26 20:51:35 UTC

Witness: 1 independent point log in to add more points →

(17, 51)

Commentary

Cremona 840f1 = LMFDB 840.d4: https://www.lmfdb.org/EllipticCurve/Q/840/d/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 840, minimal discriminant 8400, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:51:35 UTC · history