curve #2940

y² + xy = x³ − 93x − 248

a-invariants: [1, 0, 0, -93, -248]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ
conductor (N): 279775
discriminant (Δ): 26578625
Faltings height: 0.1301
naive height: 25.2121
primes of bad reduction: 5, 19, 31
regulator: 4.9813548651026408876619040602206395640292662
submitted by: David Renshaw
submitted at: 2026-09-26 20:29:18 UTC
last updated: 2026-09-26 20:29:18 UTC

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

(11, 4)
(12, 14)
(-4, 10)

Commentary

Cremona 279775c1 = LMFDB 279775.c2: https://www.lmfdb.org/EllipticCurve/Q/279775/c/2 Mordell–Weil rank exactly 3 (Cremona's tables). Conductor 279775, minimal discriminant 26578625, torsion ℤ/2ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:29:18 UTC · history