curve #2911

y² = x³ + 7x + 8

a-invariants: [0, 0, 0, 7, 8]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ
conductor (N): 4960
discriminant (Δ): -49600
Faltings height: -0.4131
naive height: 17.6820
primes of bad reduction: 2, 5, 31
regulator: 1.73332520770755389589851185967708555601069
submitted by: David Renshaw
submitted at: 2026-09-26 20:28:00 UTC
last updated: 2026-09-26 20:28:00 UTC

Witness: 2 independent points log in to add more points →

(1, 4)
(7, 20)

Commentary

Cremona 4960b1 = LMFDB 4960.b2: https://www.lmfdb.org/EllipticCurve/Q/4960/b/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 4960, minimal discriminant -49600, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:28:00 UTC · history