curve #2990

y² + xy + y = x³ − x² − 67x + 226

a-invariants: [1, -1, 1, -67, 226]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 455
discriminant (Δ): 3185
Faltings height: -0.2920
naive height: 24.2137
primes of bad reduction: 5, 7, 13
regulator: 2.473374205367291350372561411230132475652
submitted by: David Renshaw
submitted at: 2026-09-26 20:32:12 UTC
last updated: 2026-09-26 20:32:12 UTC

Witness: 1 independent point log in to add more points →

(14, 36)

Commentary

Cremona 455b1 = LMFDB 455.a3: https://www.lmfdb.org/EllipticCurve/Q/455/a/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 455, minimal discriminant 3185, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:32:13 UTC · history