curve #986

y² + xy = x³ − 34x + 68

a-invariants: [1, 0, 0, -34, 68]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/8ℤ
conductor (N): 102
discriminant (Δ): 352512
Faltings height: -0.1926
naive height: 22.1945
primes of bad reduction: 2, 3, 17
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:11:07 UTC
last updated: 2026-09-23 15:11:07 UTC

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Commentary

Cremona 102b1 = LMFDB 102.c5: https://www.lmfdb.org/EllipticCurve/Q/102/c/5 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 102, minimal discriminant 352512, torsion ℤ/8ℤ.

last edited by David Renshaw at 2026-09-23 15:11:07 UTC · history