curve #1082

y² + xy + y = x³ − 786170938x + 8484377935088

a-invariants: [1, 0, 1, -786170938, 8484377935088]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/12ℤ
conductor (N): 278070
discriminant (Δ): 33222494634354492187500
Faltings height: 3.6424
naive height: 73.0617
primes of bad reduction: 2, 3, 5, 13, 23, 31
regulator: 4.252962695109764646180575214514066619399
submitted by: David Renshaw
submitted at: 2026-09-23 15:26:10 UTC
last updated: 2026-09-23 15:26:10 UTC

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

(16198, -7612)

Commentary

Cremona 278070s4 = LMFDB 278070.s2: https://www.lmfdb.org/EllipticCurve/Q/278070/s/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 278070, minimal discriminant 33222494634354492187500, torsion ℤ/12ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:26:11 UTC · history