curve #991

y² + xy + y = x³ + x² − 25x + 39

a-invariants: [1, 1, 1, -25, 39]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/5ℤ
conductor (N): 118
discriminant (Δ): -60416
Faltings height: -0.3097
naive height: 21.3312
primes of bad reduction: 2, 59
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:11:09 UTC
last updated: 2026-09-23 15:11:09 UTC

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Commentary

Cremona 118b1 = LMFDB 118.c1: https://www.lmfdb.org/EllipticCurve/Q/118/c/1 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 118, minimal discriminant -60416, torsion ℤ/5ℤ.

last edited by David Renshaw at 2026-09-23 15:11:10 UTC · history