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curve #648

y² + y = x³ + 2x

a-invariants: [0, 0, 1, 2, 0]
rank (lower bound): ≥ 1
torsion subgroup: trivial
conductor (N): 77
discriminant (Δ): -539
Faltings height: -0.7867
naive height: 13.6930
primes of bad reduction: 7, 11
regulator: 0.09802797926446819450649012526893760873487
submitted by: David Renshaw
submitted at: 2026-09-08 19:03:25 UTC
last updated: 2026-09-08 19:03:25 UTC

Witness: 1 independent point log in to add more points →

(2, 3)

Commentary

Cremona 77a1 = LMFDB 77.a1. Curve data, generator (2, 3) and rank from the LMFDB: https://www.lmfdb.org/EllipticCurve/Q/77/a/1

last edited by David Renshaw at 2026-09-08 19:03:25 UTC · history

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