curve #2831

y² + xy = x³ − 985x + 11600

a-invariants: [1, 0, 0, -985, 11600]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 3135
discriminant (Δ): 2211350625
Faltings height: 0.5829
naive height: 32.2916
primes of bad reduction: 3, 5, 11, 19
regulator: 1.867959319870033007330448948518889446206
submitted by: David Renshaw
submitted at: 2026-09-26 20:24:24 UTC
last updated: 2026-09-26 20:24:24 UTC

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

(25, 40)

Commentary

Cremona 3135e2 = LMFDB 3135.e3: https://www.lmfdb.org/EllipticCurve/Q/3135/e/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 3135, minimal discriminant 2211350625, torsion ℤ/2ℤ × ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:24:24 UTC · history