curve #979

y² + xy + y = x³ − x² − 3002x + 63929

a-invariants: [1, -1, 1, -3002, 63929]
rank (lower bound): ≥ 0
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 90
discriminant (Δ): 6561000000
Faltings height: 0.7669
naive height: 35.6344
primes of bad reduction: 2, 3, 5
regulator: 1
submitted by: David Renshaw
submitted at: 2026-09-23 15:10:02 UTC
last updated: 2026-09-23 15:10:02 UTC

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Commentary

Cremona 90c6 = LMFDB 90.c3: https://www.lmfdb.org/EllipticCurve/Q/90/c/3 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 90, minimal discriminant 6561000000, torsion ℤ/2ℤ × ℤ/6ℤ.

last edited by David Renshaw at 2026-09-23 15:10:03 UTC · history