curve #3006

y² + y = x³ − x² + 4790x + 136798

a-invariants: [0, -1, 1, 4790, 136798]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/5ℤ
conductor (N): 87515
discriminant (Δ): -15306428196875
Faltings height: 1.2160
naive height: 37.1989
primes of bad reduction: 5, 23, 761
regulator: 9.47197071070601930064228082236823597463274
submitted by: David Renshaw
submitted at: 2026-09-26 20:33:01 UTC
last updated: 2026-09-26 20:33:01 UTC

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

(64, 837)
(139, 1862)

Commentary

Cremona 87515b1 = LMFDB 87515.a2: https://www.lmfdb.org/EllipticCurve/Q/87515/a/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 87515, minimal discriminant -15306428196875, torsion ℤ/5ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:33:01 UTC · history