curve #987

y² + xy = x³ − 114x − 396

a-invariants: [1, 0, 0, -114, -396]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 102
discriminant (Δ): 30338064
Faltings height: 0.1539
naive height: 25.8227
primes of bad reduction: 2, 3, 17
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:11:08 UTC
last updated: 2026-09-23 15:11:08 UTC

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Commentary

Cremona 102b2 = LMFDB 102.c4: https://www.lmfdb.org/EllipticCurve/Q/102/c/4 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 102, minimal discriminant 30338064, torsion ℤ/2ℤ × ℤ/4ℤ.

last edited by David Renshaw at 2026-09-23 15:11:08 UTC · history