curve #2849

y² + xy + y = x³ + x² − 43400x + 3397385

a-invariants: [1, 1, 1, -43400, 3397385]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 18690
discriminant (Δ): 192320100000000
Faltings height: 1.5300
naive height: 43.6482
primes of bad reduction: 2, 3, 5, 7, 89
regulator: 1.532262183558395160655384273741095404155
submitted by: David Renshaw
submitted at: 2026-09-26 20:25:12 UTC
last updated: 2026-09-26 20:25:12 UTC

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

(135, 79)

Commentary

Cremona 18690m1 = LMFDB 18690.l5: https://www.lmfdb.org/EllipticCurve/Q/18690/l/5 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 18690, minimal discriminant 192320100000000, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:25:12 UTC · history