curve #2842

y² + xy + y = x³ − x² + 20x + 22

a-invariants: [1, -1, 1, 20, 22]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/4ℤ
conductor (N): 275
discriminant (Δ): -859375
Faltings height: -0.1741
naive height: 20.6473
primes of bad reduction: 5, 11
regulator: 2.384490492426557628481549642854394937146
submitted by: David Renshaw
submitted at: 2026-09-26 20:24:52 UTC
last updated: 2026-09-26 20:24:52 UTC

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

(8, 21)

Commentary

Cremona 275a1 = LMFDB 275.a4: https://www.lmfdb.org/EllipticCurve/Q/275/a/4 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 275, minimal discriminant -859375, torsion ℤ/4ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:24:52 UTC · history