curve #2704

y² + y = x³ − 49x + 132

a-invariants: [0, 0, 1, -49, 132]
rank (lower bound): ≥ 3
torsion subgroup: trivial
conductor (N): 26171
discriminant (Δ): -26171
Faltings height: -0.2651
naive height: 23.2925
primes of bad reduction: 26171
regulator: 0.76741106056686255182221044745366575448361628
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:18:32 UTC
last updated: 2026-09-26 20:18:32 UTC

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

(4, 0)
(3, 3)
(5, 3)

Commentary

Cremona 26171a1 = LMFDB 26171.a1: https://www.lmfdb.org/EllipticCurve/Q/26171/a/1 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 26171, minimal discriminant -26171, torsion trivial. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:36:54 UTC · history