curve #2702

y² + xy + y = x³ − x² − 6x + 12

a-invariants: [1, -1, 1, -6, 12]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 39023
discriminant (Δ): -39023
Faltings height: -0.4293
naive height: 18.2903
primes of bad reduction: 39023
regulator: 1.2676518356606668794268217392553456420832999
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:18:25 UTC
last updated: 2026-09-26 20:18:25 UTC

Witness: 3 independent points log in to add more points →

(2, 1)
(0, 3)
(3, 2)

Commentary

Cremona 39023a1 = LMFDB 39023.a1: https://www.lmfdb.org/EllipticCurve/Q/39023/a/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 39023, minimal discriminant -39023, torsion trivial. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:36:34 UTC · history