curve #2813

y² + xy + y = x³ − 2708x + 61518

a-invariants: [1, 0, 1, -2708, 61518]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/3ℤ
conductor (N): 356590
discriminant (Δ): -376648187500
Faltings height: 0.9476
naive height: 35.5846
primes of bad reduction: 2, 5, 13, 211
regulator: 3.0947096830247695209214061492047590846080619
submitted by: David Renshaw
submitted at: 2026-09-26 20:23:35 UTC
last updated: 2026-09-26 20:23:35 UTC

Witness: 3 independent points log in to add more points →

(39, 105)
(27, 77)
(-61, 5)

Commentary

Cremona 356590d1 = LMFDB 356590.d1: https://www.lmfdb.org/EllipticCurve/Q/356590/d/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 356590, minimal discriminant -376648187500, torsion ℤ/3ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:23:35 UTC · history