curve #3331

y² + xy + y = x³ + x² − 5199564x + 4561336557

a-invariants: [1, 1, 1, -5199564, 4561336557]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/8ℤ
conductor (N): 4794
discriminant (Δ): 6798517395939072
Faltings height: 2.3797
naive height: 58.0059
primes of bad reduction: 2, 3, 17, 47
regulator: 5.986482453135215741486651132037266990940
submitted by: David Renshaw
submitted at: 2026-09-26 20:59:02 UTC
last updated: 2026-09-26 20:59:02 UTC

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

(2309, 68649)

Commentary

Cremona 4794e4 = LMFDB 4794.c2: https://www.lmfdb.org/EllipticCurve/Q/4794/c/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 4794, minimal discriminant 6798517395939072, torsion ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:59:02 UTC · history