curve #2713

y² + y = x³ − x² − 4x + 10

a-invariants: [0, -1, 1, -4, 10]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 28571
discriminant (Δ): -28571
Faltings height: -0.4585
naive height: 17.8823
primes of bad reduction: 28571
regulator: 1.2231261170461095956013967947315288068928580
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:18:54 UTC
last updated: 2026-09-26 20:18:54 UTC

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

(1, 2)
(2, 2)
(-1, 3)

Commentary

Cremona 28571a1 = LMFDB 28571.a1: https://www.lmfdb.org/EllipticCurve/Q/28571/a/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 28571, minimal discriminant -28571, torsion trivial. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:20:48 UTC · history