curve #2984

y² + xy + y = x³ + x² − 14x + 26

a-invariants: [1, 1, 1, -14, 26]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 777
discriminant (Δ): -266511
Faltings height: -0.2616
naive height: 20.4558
primes of bad reduction: 3, 7, 37
regulator: 1.748805510252616867776149934880211141245
submitted by: David Renshaw
submitted at: 2026-09-26 20:31:53 UTC
last updated: 2026-09-26 20:31:53 UTC

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

(4, 5)

Commentary

Cremona 777d1 = LMFDB 777.c4: https://www.lmfdb.org/EllipticCurve/Q/777/c/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 777, minimal discriminant -266511, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:31:53 UTC · history