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curve #675

y² + y = x³ − 19x + 60

a-invariants: [0, 0, 1, -19, 60]
rank (lower bound): ≥ 4
torsion subgroup: trivial
conductor (N): 1129211
discriminant (Δ): -1129211
Faltings height: -0.1468
naive height: 21.7202
primes of bad reduction: 1129211
regulator: 4.312445190909356061684590638879207982242075125
submitted by: David Renshaw
submitted at: 2026-09-08 19:27:00 UTC
last updated: 2026-09-08 19:27:00 UTC

Witness: 4 independent points log in to add more points →

(2, 5)
(1, 6)
(3, 5)
(-3, 9)

Commentary

LMFDB 1129211.a1. Curve data, generators (2, 5), (1, 6), (3, 5), (-3, 9) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/1129211/a/1

last edited by David Renshaw at 2026-09-08 19:27:00 UTC · history

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