curve #999

y² + y = x³ − x² + 10x + 6

a-invariants: [0, -1, 1, 10, 6]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/5ℤ
conductor (N): 155
discriminant (Δ): -96875
Faltings height: -0.3562
naive height: 18.4197 ☆ record for ℤ/5ℤ torsion, rank ≥ 1
primes of bad reduction: 5, 31
regulator: 1.514887282206749682835235426532428402510
submitted by: David Renshaw
submitted at: 2026-09-23 15:13:16 UTC
last updated: 2026-09-23 15:13:16 UTC

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

(2, 5)

Commentary

Cremona 155a1 = LMFDB 155.a2: https://www.lmfdb.org/EllipticCurve/Q/155/a/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 155, minimal discriminant -96875, torsion ℤ/5ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:13:16 UTC · history