curve #3315

y² + xy = x³ − x² − 1017x + 8883

a-invariants: [1, -1, 0, -1017, 8883]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/6ℤ
conductor (N): 306
discriminant (Δ): 35192575602
Faltings height: 0.7288
naive height: 32.3880
primes of bad reduction: 2, 3, 17
regulator: 3.375774058960775017698094599590825063296
submitted by: David Renshaw
submitted at: 2026-09-26 20:56:27 UTC
last updated: 2026-09-26 20:56:27 UTC

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

(7, 42)

Commentary

Cremona 306b4 = LMFDB 306.a1: https://www.lmfdb.org/EllipticCurve/Q/306/a/1 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 306, minimal discriminant 35192575602, torsion ℤ/6ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:56:27 UTC · history