curve #3134

y² + xy + y = x³ + x² − 201x + 198

a-invariants: [1, 1, 1, -201, 198]
rank (lower bound): ≥ 2
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 22035
discriminant (Δ): 485541225
Faltings height: 0.3578
naive height: 27.5238
primes of bad reduction: 3, 5, 13, 113
regulator: 2.79216356466533004739912261607736493849129
submitted by: David Renshaw
submitted at: 2026-09-26 20:38:51 UTC
last updated: 2026-09-26 20:38:51 UTC

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

(14, 12)
(16, 29)

Commentary

Cremona 22035c2 = LMFDB 22035.e2: https://www.lmfdb.org/EllipticCurve/Q/22035/e/2 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 22035, minimal discriminant 485541225, torsion ℤ/2ℤ × ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:38:51 UTC · history