curve #2903

y² + xy + y = x³ − x² − 3x + 2

a-invariants: [1, -1, 1, -3, 2]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ
conductor (N): 145
discriminant (Δ): 145
Faltings height: -0.8365
naive height: 14.5794
primes of bad reduction: 5, 29
regulator: 0.5844576298645671120707842100216479683223
submitted by: David Renshaw
submitted at: 2026-09-26 20:27:39 UTC
last updated: 2026-09-26 20:27:39 UTC

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

(0, 1)

Commentary

Cremona 145a1 = LMFDB 145.a1: https://www.lmfdb.org/EllipticCurve/Q/145/a/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 145, minimal discriminant 145, torsion ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:27:39 UTC · history