curve #3113

y² + xy + y = x³ − x² − 105x + 272

a-invariants: [1, -1, 1, -105, 272]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 275
discriminant (Δ): 47265625
Faltings height: 0.1725
naive height: 25.5665
primes of bad reduction: 5, 11
regulator: 1.192245246213278814240774821427197468573
submitted by: David Renshaw
submitted at: 2026-09-26 20:37:53 UTC
last updated: 2026-09-26 20:37:53 UTC

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

(0, 16)

Commentary

Cremona 275a2 = LMFDB 275.a3: https://www.lmfdb.org/EllipticCurve/Q/275/a/3 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 275, minimal discriminant 47265625, torsion ℤ/2ℤ × ℤ/2ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:37:53 UTC · history