curve #3311

y² + y = x³ − x² − 233100x + 43395156

a-invariants: [0, -1, 1, -233100, 43395156]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/5ℤ
conductor (N): 199595
discriminant (Δ): -1826418996875
Faltings height: 1.6295
naive height: 48.6913
primes of bad reduction: 5, 11, 19, 191
regulator: 7.24194430913651360628349414528870041204051
submitted by: David Renshaw
submitted at: 2026-09-26 20:55:48 UTC
last updated: 2026-09-26 20:55:48 UTC

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

(300, 612)
(277, 60)

Commentary

Cremona 199595a1 = LMFDB 199595.b1: https://www.lmfdb.org/EllipticCurve/Q/199595/b/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 199595, minimal discriminant -1826418996875, torsion ℤ/5ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:55:48 UTC · history