curve #1079

y² + xy = x³ − 673039570x − 5895575919100

a-invariants: [1, 0, 0, -673039570, -5895575919100]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 249690
discriminant (Δ): 4496908623986020832100000000
Faltings height: 4.0338
naive height: 72.5955
primes of bad reduction: 2, 3, 5, 7, 29, 41
regulator: 4.745614618301898279040255863883040063116
submitted by: David Renshaw
submitted at: 2026-09-23 15:26:08 UTC
last updated: 2026-09-23 15:26:08 UTC

Witness: 1 independent point log in to add more points →

(29720, 579230)

Commentary

Cremona 249690cj2 = LMFDB 249690.cj6: https://www.lmfdb.org/EllipticCurve/Q/249690/cj/6 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 249690, minimal discriminant 4496908623986020832100000000, torsion ℤ/2ℤ × ℤ/8ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-23 15:26:08 UTC · history