curve #2860

y² + xy = x³ − 64482970x + 199297549412

a-invariants: [1, 0, 0, -64482970, 199297549412]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/10ℤ
conductor (N): 359310
discriminant (Δ): 157579868246774400000
Faltings height: 3.0707
naive height: 65.5593
primes of bad reduction: 2, 3, 5, 7, 29, 59
regulator: 2.651674263151548184751257310682681398444
submitted by: David Renshaw
submitted at: 2026-09-26 20:25:42 UTC
last updated: 2026-09-26 20:25:42 UTC

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

(4604, 1358)

Commentary

Cremona 359310bp1 = LMFDB 359310.bp2: https://www.lmfdb.org/EllipticCurve/Q/359310/bp/2 Mordell–Weil rank exactly 1 (Cremona's tables). Conductor 359310, minimal discriminant 157579868246774400000, torsion ℤ/10ℤ. The witness is the generator from Cremona's tables.

last edited by David Renshaw at 2026-09-26 20:25:43 UTC · history