curve #2929

y² = x³ + x² − 79x − 63

a-invariants: [0, 1, 0, -79, -63]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
conductor (N): 214912
discriminant (Δ): 31377152
Faltings height: 0.1283
naive height: 24.7346
primes of bad reduction: 2, 23, 73
regulator: 6.3153346861019614796392101114828234018194451
submitted by: David Renshaw
submitted at: 2026-09-26 20:28:49 UTC
last updated: 2026-09-26 20:28:49 UTC

Witness: 3 independent points log in to add more points →

(-1, 4)
(-7, 14)
(9, 6)

Commentary

Cremona 214912a1 = LMFDB 214912.a2: https://www.lmfdb.org/EllipticCurve/Q/214912/a/2 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 214912, minimal discriminant 31377152, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:28:49 UTC · history