curve #2711

y² + y = x³ + x² − 4x + 8

a-invariants: [0, 1, 1, -4, 8]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 35083
discriminant (Δ): -35083
Faltings height: -0.4424
naive height: 18.0586
primes of bad reduction: 35083
regulator: 1.2364281089527077263843947167679416335068828
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:18:50 UTC
last updated: 2026-09-26 20:18:50 UTC

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

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

Commentary

Cremona 35083c1 = LMFDB 35083.a1: https://www.lmfdb.org/EllipticCurve/Q/35083/a/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 35083, minimal discriminant -35083, torsion trivial. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:20:57 UTC · history